Author links open overlay panel xiying zheng a bo kong b. It can handle text and images, outlines, text annotations, link annotations, embedded png and jpeg images, embedded type 1 and truetype fonts, encrypted pdf files, a variety of character sets and encodings, etc. Request pdf quantum codes obtained from constacyclic codes in this article, by using hermitian construction, we obtain several new quantum codes and quantum mds codes compare to the known. Constacyclic codes are an important class of linear codes in coding theory. The quadraticresidue qr codes 9, 5, x, 2 are cyclic codes of prime block length p over a field gfl, where 1 is another prime which is a quadratic residue modulo p. Among other results, we also consider the euclidean and hermitian dual codes of skew cyclic and skew negacyclic codes over finite chain rings in general and over in particular. We show that if cis self orthogonal so is c and we obtain in the gray images of cyclic and quasicyclic. Constacyclic codes of length t p s let f q be a finite field of order q p m and f a. Bayram and siap 4,5 studied constacyclic codes over the ring fpuhup. The first one is obtained via the gray map and the calderbankshorsteane construction.
You also get unlimited file sizes as well as the ability to upload and convert several files to pdf at the same time. Recently, in, sharma explicitly determined the generator polynomials of all repeatedroot constacyclic codes of length l t p s over f p m and their dual codes. Cyclic and some constacyclic codes over the ring z4u. Code of practice for architectural and building drawings. Cyclic codes over local frobenius rings of order 16. The international code council icc is a nonprofit organization dedicated to developing model codes and standards used in the design, build and compliance process. Instead, they refer to dots and dashes because thats a convenient way of showing the codes on the printed page. Jul 19, 20 this paper is devoted to the study of selfdual codes arising from constacyclic codes. Skew constacyclic codes over finite fields and finite. I cannot adequately express how go od this book really is. By giving two product, it is investigated their duality. Firstly, quasi constacyclic and skew quasi constacyclic codes are introduced. General requirements for screed board concrete vibrators. The structure of skew constacyclic codes and their duals are provided.
Constacyclic codes are preferred in engineering due to their e cient encoding process via shift registers. As an application of these necessary and sufficient conditions, some conditions under which mds hermitian selforthogonal and selfdual constacyclic codes. Code is structuredis probably not as hard as most people might think. Jacodesmath aims to provide a free medium to the research community on both quality and time. Finite fields and their applications 18 2012 1217a1231 table 1 i. Journal of algebra combinatorics discrete structures and applications the main goal of jacodesmath is to present the most recent research in algebra both pure and applied. Pdf cyclic and constacyclic codes over a nonchain ring. On some classes of constacyclic codes over polynomial residue rings. There is certainly a lot going on inside the modern computer, but it is a lot of very common and simple operations. The hidden language of computer hardware and software. Although computers today are more complex than the.
The gen erator polynomials of this kind of codes of length. Polyadic constacyclic codes article pdf available in ieee transactions on information theory 619 july 2014 with 4,621 reads how we measure reads. Then yc is a quasi constacyclic code of index 4 and of length 4n. By using two inner product, it is investigated the duality about quasiconstacyclic and skew quasiconstacyclic codes over r. Do nonfree lcd codes over finite commutative frobenius rings. A sufficient condition for 1generator skew quasi constacyclic codes to be free is determined. From the method, we can get not only those known quantum mds codes from constacyclic codes but also a new class of quantum mds code from hermitian dualcontaining mds constacyclic code. The structure of the ambient ring of polycyclic codes over grpa,m and generating sets for its ideals are considered. Further related topics such as discrete mathematics, combinatorics, cryptography, coding, graph theory, etc. Firstly, quasiconstacyclic and skew quasiconstacyclic codes over r are introduced. Jacodesmath extends its condolences to the losses of jacodesmath community and all world due to this outbreak, and wishes a rapid recovery to those who are infected and wish health to the all world.
You will be redirected to the full text document in the repository in a few seconds, if not click here. In this paper, we study skew cyclic and skew constacyclic codes over the ring. A code over r of length n is a nonempty subset of r n, and a code is linear over r of length n if it is an rsubmodule of r n. Lee weights of elements of sand lee distance in the linear codes over s. Access the most up to date content in iso standards, graphical symbols, codes or terms and definitions. Journal of algebra combinatorics discrete structures and. Many optimal linear codes are directly derived from constacyclic codes. Jacodesmath is now growing stronger in its fourth year with its strong editorial board and quality of papers published.
The class of constacyclic codes contains cyclic and negacyclic codes which have been studied for a long time 2. In this paper, we classify repeatedroot constacyclic codes of length. Advances in mathematics of communications, 2017, 11 1. This allows us to express generators of euclidean and hermitian dual codes of skew cyclic and skew negacyclic codes in terms of the generators of the original codes. This paper overviews the study of skew constacyclic codes over finite fields and finite commutative chain rings. A class of constacyclic codes over a finite field core reader. Information message description 100 continue only a part of the request has been received by the server, but as long as it has. The hour of code is a global movement reaching tens of millions of students. Constacyclic codes form an interesting family of errorcorrecting codes due to their rich algebraic structure, and are generalizations of cyclic and negacyclic codes.
Skew constacyclic codes over finite fields and finite chain rings. Cyclic and constacyclic codes over a nonchain ring 8. After presenting preliminary concepts in section 2, we study skew negacyclic, cyclic, and constacyclic codes over finite fields in section 3. As an application of these necessary and sufficient conditions, some conditions under which mds hermitian. On selfdual constacyclic codes over finite fields springerlink. It is known that r is a chain ring with the unique maximal ideal u f p m. Constacyclic codes over finite fields sciencedirect. We also prove that this class of constacyclic codes over the ring is principally generated. Constacyclic code, generator polynomial, selfdual code, gray map. Since fqx is a free fqalgebra with x as a free generator. Code complete is a pretty lame title for a work of brilliance. This paper is devoted to the study of selfdual codes arising from constacyclic codes. On depth spectra of constacyclic codes over finite.
Hulls of linear codes have been extensively studied due to their wide applications and links with the efficiency of some algorithms in coding theory. On the structure of constacyclic codes of length p over. We have introduced some new gray maps and determined the relation between codes using the. Skew cyclic and skew constacyclic codes over the ring p. In this section, we consider constacyclic codes of length t p s over f q, where is a prime integer fferent from p and s, t are nonnegative integers. Han cyclic codes 12 generator and paritycheck matrices. Quantum mds codes have been studied 7,8,11 using constacyclic codes and bch like constacyclic codes. We also show that a free constacyclic code c over finite chain ring is lcd code if and only if c is reversible. On the structure of constacyclic codes of length p over u k. Based on constacyclic codes over fq2, we derive four new families of quantum mds codes, one of which is an explicit generalization of the construction given in theorem 7 in 22. We determine the form of the generators of the cyclic codes over this ring and their spanning sets.
Quantum codes from constacyclic codes over the ring fqu1. The average hull dimension of negacyclic codes over finite fields. January issue 1may issue 2september issue 3 announcements. With a free trial of our online pdf converter, you can convert files to and from pdf for free, or sign up for one of our memberships for limitless access to our file converters full suite of tools. In section 4 and section 5, by using the structure obtained in section 3 the hamming and homogeneous distances of all. These codes possess rich algebraic structures and can be e. More generally, cyclic codes over the ring r k were investigated in dougherty et al. A class of constacyclic codes over a finite fieldii. In 2015, raka studied repeated root constacyclic codes of length l t p s over f q in. The structure of all skew constacyclic codes is completely determined. Its the only pdf viewer that can open and interact with all types of pdf content, including. On the other hand, in the literature there exist a few papers which study group ring encodings 8.
This journal is an online journal and free of charge to all parties. This paper is devoted to the study of the construction of new quantum mds codes. Although morse code has absolutely nothing to do with computers, becoming familiar with the nature. Pdf skew constacyclic codes over finite chain rings. Do nonfree lcd codes over finite commutative frobenius rings exist. The gray image of skew quasiconstacyclic codes over r is determined.
Here, the authors mainly further generalize the results in 4 to co des over the ring z p v h v p. Repeatedroot constacyclic codes of length 3lps and their. We later show that a free constacyclic code over finite chain ring is lcd if and only if it is reversible, and also provide a necessary and sufficient. Quantum codes obtained from constacyclic codes request pdf.
The complete reference every half an age or so, you come across a book that shortcircuits th e school of experience and saves you years of purgatory. This is a surprising amount, as constacyclic codes have already been extensively researched. In this paper we extend results of 15 and discuss 1. The other contributions are the characterizations of projection of lcd codes see theorem 3 and lift lcd codes see theorem 4 over a finite commutative local frobenius ring. Many of these pdf documents are very large and may take a long time to open depending on the internet connection speed. Adobe acrobat reader dc software is the free global standard for reliably viewing, printing, and commenting on pdf documents. On the structure of constacyclic codes of length ps 509 proposition 3. Then c is a constacyclic code over r if and only if c 1,c 2,c 3,c 4 are a. In morse code, every letter of the alphabet corresponds to a short series of dots and dashes, as you can see in the following table. We derive the generators of constacyclic and dual constacyclic codes. Only the cases 1 2 and 3 have been studied to any extent. Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes. And now, its connected to the adobe document cloud. Many authors such as 8 worked on constacyclic codes over.
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