On LCD Negacyclic Codes over Finite Fields

Pang, Binbin; Zhu, Shixin; Sun, Zhonghua

doi:10.1007/s11424-017-6301-7

Cited by 30 publications

(13 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this paper, we study some classes of MDS negacyclic LCD codes of length n| q−1 2 , n| q+1 2 and some classes of negacyclic LCD codes of length n = q + 1. In Theorem 8 we give a corrected and generalized of the result of Theorem 6.1 in [24]. We also obtain some classes of q 2 -ary Hermitian MDS negacyclic LCD codes of length n| (q − 1) and some classes of q 2 -ary Hermitian negacyclic LCD codes n = q 2 + 1.…”

Section: Resultsmentioning

confidence: 93%

See 1 more Smart Citation

On MDS negacyclic LCD codes

Koroglu¹,

Sarı²

2019

Filomat

View full text Add to dashboard Cite

Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and detecting capabilities for fixed length and dimension. The construction of linear codes that are both LCD and MDS is a hard task in coding theory. In this paper, we study the constructions of LCD codes that are MDS from negacyclic codes over finite fields of odd prime power q elements. We construct four families of MDS negacyclic LCD codes of length n| q−1 2 , n| q+1 2 and a family of negacyclic LCD codes of length n = q − 1. Furthermore, we obtain five families of q 2 -ary Hermitian MDS negacyclic LCD codes of length n| (q − 1) and four families of Hermitian negacyclic LCD codes of length n = q 2 + 1. For both Euclidean and Hermitian cases the dimensions of these codes are determined and for some classes the minimum distances are settled. For the other cases, by studying q and q 2 -cyclotomic classes we give lower bounds on the minimum distance.

show abstract

Section: Resultsmentioning

confidence: 93%

“…Guneri et al introduced Hermitian LCD codes in [11]. In [24], a class of MDS negacyclic LCD codes of even length n| q − 1 has been given. Carlet and Guiley have studied an application of LCD codes against side-channel attacks, and have presented particular constructions for LCD codes in [3].…”

Section: Introductionmentioning

confidence: 99%

On MDS negacyclic LCD codes

Koroglu¹,

Sarı²

2019

Filomat

View full text Add to dashboard Cite

show abstract

“…We believe that our results will shed light on BCH codes and cyclic codes. It is also hoped that these results will work to discuss constructions of LCD codes from negacyclic codes over finite fields as did in [20].…”

Section: Resultsmentioning

confidence: 96%

Some binary BCH codes with length n = 2  + 1

Liu

et al. 2019

Finite Fields and Their Applications

View full text Add to dashboard Cite

Under research for near sixty years, Bose-Ray-Chaudhuri-Hocquenghem(BCH) codes have played increasingly important roles in many applications such as communication systems, data storage and information security. However, the dimension and minimum distance of BCH codes are seldom solved until now because of their intractable characteristics. The objective of this paper is to study the dimensions of some BCH codes of length n = 2 m + 1 with m = 2t + 1, 4t + 2, 8t + 4 and m ≥ 10. Some new techniques are employed to investigate coset leaders modulo n. For each type of m above, the first five largest coset leaders modulo n are determined, the dimension of some BCH codes of length n with designed distance δ > 2 ⌈ m 2 ⌉ is presented. These new techniques and results may be helpful to study other families of cyclic codes over finite fields.

show abstract

“…Pang 等 [18] 利用负循环码构造了几类 LCD MDS 码, 相关结果总结如下. 定理 4.20 设 q 是奇素数幂, n 是正整数, 则下列条件之一成立时, 存在 q 元 [n, k] 负循环 LCD MDS 码:…”

Section: Trs Lcd Mds 码unclassified