نتایج جستجو برای: cyclic codes

تعداد نتایج: 173811  

2007
M. Moisio K. Ranto K. Väänänen

This paper considers the weight distributions of binary cyclic codes with one or two zeros and hyper-Kloosterman codes. The results on value distributions of certain monomial exponential sums and connections between exponential sums and Kloosterman sums are applied together with the Pless power moment identity in these conciderations. Explicit formulae for the number of low-weight codewords are...

Journal: :CoRR 2017
Alexandre Zhdanov

In this paper we obtain at least 61 new singly even (Type I) binary [72,36,12] self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes) and at least 13 new doubly even (Type II) binary [72,36,12] self-dual codes by replacing the first row in each circulant in a double circulant code by "all ones" and "all zeros" vectors respectively. Keywords—convolutional encoding, qu...

2013
Jian Gao Linzhi Shen Fang-Wei Fu

Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring Fq + uFq, where u 2 = 0, q = p, n a positive integer and p a prime number, are investigated. By the Chinese Remainder Theorem, structural properties and the decomposition of GQC codes are given. For 1-generator GQC codes, minimal generating sets and lower bounds on the minimum distance are given. As a special class of GQC...

Journal: :CoRR 2013
Jian Gao Fang-Wei Fu Linzhi Shen

Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring Fq + uFq, where u 2 = 0, q = p, n a positive integer and p a prime number, are investigated. By the Chinese Remainder Theorem, structural properties and the decomposition of GQC codes are given. For 1-generator GQC codes, minimal generating sets and lower bounds on the minimum distance are given. As a special class of GQC...

Journal: :Des. Codes Cryptography 2014
Alexander Zeh Sergey Bezzateev

A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann–Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. Furthermore, we refine our bound for several families of cyclic codes. We define syndro...

Journal: :IEEE Trans. Information Theory 2001
San Ling Patrick Solé

A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese Remainder Theorem (CRT), or of the Discrete Fourier Transform (DFT), that ring can be decomposed into a direct product of fields. That ring decomposition in turn yields a code construction from codes of lower ...

Journal: :CoRR 2015
Nabil Bennenni Kenza Guenda Sihem Mesnager

This paper is dealing with DNA cyclic codes which play an important role in DNA computing and have attracted a particular attention in the literature. Firstly, we introduce a new family of DNA cyclic codes over the ring R = F2[u]/(u ). Such codes have theoretical advantages as well as several applications in DNA computing. A direct link between the elements of such a ring and the 64 codons used...

Journal: :IEEE Trans. Information Theory 1999
Alexis Bonnecaze Parampalli Udaya

We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u 2 = 0. This ring shares many properties of Z 4 and F 4 and admits a linear "Gray map". Cyclic codes are described as modules over (F 2 + uF 2) n which may not be free. Self-dual codes of odd length exists as in the case of Z 4-codes. We exhibit some extremal codes of this very interesting family.

2015
Hai Q. Dinh Chengju Li Qin Yue

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distribu...

Journal: :IEEE Trans. Information Theory 2003
T. Kiran B. Sundar Rajan

We study -length Abelian codes over Galois rings with characteristic , where and are relatively prime, having the additional structure of being closed under the following two permutations: i) permutation effected by multiplying the coordinates with a unit in the appropriate mixed-radix representation of the coordinate positions and ii) shifting the coordinates by positions. A code is -quasi-cyc...

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