New binary h-generator quasi-cyclic codes by augmentation and new minimum distance bounds

Chen, Eric Zhi

doi:10.1007/s10623-015-0059-5

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…Although it is quite difficult to improve the binary codes, we have made a total of 23 improvements on [13]. It should also be noted that these codes (and ones given in [10]) are only special cases of h-generator QC codes. Further investigation on general h-generator QC codes is promising.…”

Section: Discussionmentioning

confidence: 99%

“…In fact, they are 2-generator QC codes. In [6,10], construction methods have been presented to obtain h-generator QC codes with improved minimum distances.…”

Section: Quasi-cyclic Codes and Their Computer Constructionsmentioning

confidence: 99%

“…As demonstrated in [6,7,10], it is often possible to extend the QC codes by adding one or more rows to the generator matrix of a 1-generator QC code. For example, with m = 57, a new binary 1-generator QC [228, 18,96] code was constructed [7], with the defining polynomials g 1 (x)= 4524727255730403632, g 2 (x)= 5052140564035060426, g 3 (x)= 3041362270077724243, and g 4 (x)= 6624210767535636614.…”

Section: Quasi-cyclic Codes and Their Computer Constructionsmentioning

confidence: 99%

“…was obtained, where 1 is a vector of 57 1's, and 0 is a vector of 57 0's, and G i are the circulant matrix defined by the polynomial g i (x), i = 1, 2, 3, 4. With this motivation, the known good QC codes in [9,13] have been investigated to obtain good augmented h-generator QC codes, and many good h-generator QC codes have constructed in [10].…”

Section: Quasi-cyclic Codes and Their Computer Constructionsmentioning

confidence: 99%

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Some new binary codes with improved minimum distances

CHEN¹

2018

Journal of Algebra Combinatorics Discrete Structures and Applications

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It has been well-known that the class of quasi-cyclic (QC) codes contain many good codes. In this paper, a method to conduct a computer search for binary 2-generator QC codes is presented, and a large number of good 2-generator QC codes have been obtained. 5 new binary QC codes that improve the lower bounds on minimum distance are presented. Furthermore, with new 2-generator QC codes and Construction X, 2 new improved binary linear codes are obtained. With the standard construction techniques, another 16 new binary linear codes that improve the lower bound on the minimum distance have also been obtained.2010 MSC: 94B05, 94B65

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Section: Discussionmentioning

confidence: 99%

“…In fact, they are 2-generator QC codes. In [6,10], construction methods have been presented to obtain h-generator QC codes with improved minimum distances.…”

Section: Quasi-cyclic Codes and Their Computer Constructionsmentioning

confidence: 99%

Section: Quasi-cyclic Codes and Their Computer Constructionsmentioning

confidence: 99%

Section: Quasi-cyclic Codes and Their Computer Constructionsmentioning

confidence: 99%

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Some new binary codes with improved minimum distances

CHEN¹

2018

Journal of Algebra Combinatorics Discrete Structures and Applications

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“…Two-dimensional (2D, for short) cyclic codes which have a long history, see for example [12,13], still gain attention, see [9-11, 22, 23] and the references therein. As mentioned in [9], these codes are special cases of quasi-cyclic codes which form an important and well-studied class of codes (see, for example, [1,3,7,18,21,25] and their references). Also constacyclic codes which are a generalization of cyclic codes are investigated over finite fields and some other types of rings, see [5,24] and their references.…”

Section: Introductionmentioning

confidence: 99%

One-Sided Repeated-Root Two-Dimensional Cyclic and Constacyclic Codes

Khormaei¹,

Nikseresht²,

Namazi³

2022

Preprint

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In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field F = F q . We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate when such codes are self-dual. Moreover, we prove that if there exists an asymptotically good family of one-sided repeated-root two-dimensional cyclic or constacyclic codes, then there exists an asymptotically good family of simple root two-dimensional cyclic or constacyclic codes with parameters at least as good as the first family. Furthermore, we show that several of the main results of the papers Rajabi and Khashyarmanesh (2018) [20] and Sepasdar and Khashyarmanesh (2016) [23] are not accurate and find other conditions needed for them to hold.

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