共查询到20条相似文献,搜索用时 15 毫秒
2.
Zhengchun Zhou 《Designs, Codes and Cryptography》2018,86(11):2513-2523
Linear codes with a few weights have applications in data storage systems, secret sharing schemes, and authentication codes. Recently, Ding (IEEE Trans. Inf. Theory 61(6):3265–3275, 2015) proposed a class of ternary linear codes with three weights from a family of cyclic difference sets in \(({\mathbb {F}}_{3^m}^*/{\mathbb {F}}_{3}^*,\times )\), where \(m=3k\) and k is odd. One objective of this paper is to construct ternary linear codes with three weights from cyclic difference sets in \(({\mathbb {F}}_{3^m}^*/{\mathbb {F}}_{3}^*,\times )\) derived from the Helleseth–Gong functions. This construction works for any positive integer \(m=sk\) with an odd factor \(s\ge 3\), and thus leads to three-weight ternary linear codes with more flexible parameters than earlier ones mentioned above. Another objective of this paper is to determine the weight distribution of the proposed linear codes. 相似文献
3.
Gennian Ge 《Discrete Mathematics》2008,308(13):2704-2708
In this note, we consider a construction for optimal ternary constant weight codes (CWCs) via Bhaskar Rao designs (BRDs). The known existence results for BRDs are employed to generate many new optimal nonlinear ternary CWCs with constant weight 4 and minimum Hamming distance 5. 相似文献
4.
Chengju Li 《Designs, Codes and Cryptography》2018,86(10):2261-2278
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. It was proved that asymptotically good Hermitian LCD codes exist. The objective of this paper is to construct some cyclic Hermitian LCD codes over finite fields and analyse their parameters. The dimensions of these codes are settled and the lower bounds on their minimum distances are presented. Most Hermitian LCD codes presented in this paper are not BCH codes. 相似文献
5.
6.
Combinatorial ‐designs have wide applications in coding theory, cryptography, communications, and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a ‐design. In this paper, we first determine the weight distributions of a class of linear codes derived from the dual of some extended cyclic codes. We then obtain infinite families of 2‐designs and explicitly compute their parameters from the supports of all the codewords with a fixed weight in the codes. By a simple counting argument, we obtain exponentially many 2‐designs. 相似文献
7.
8.
9.
Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm . 相似文献
10.
《Discrete Mathematics》2023,346(7):113391
Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. One of the central themes in symbol-pair coding theory is the constructions of symbol-pair codes with the largest possible minimum symbol-pair distance. Maximum distance separable (MDS) and almost maximum distance separable (AMDS) symbol-pair codes are optimal and sub-optimal regarding the Singleton bound, respectively. In this paper, six new classes of AMDS symbol-pair codes are explicitly constructed through repeated-root cyclic codes. Remarkably, one class of such codes has unbounded lengths and the minimum symbol-pair distance of another class can reach 13. 相似文献
11.
Designs, Codes and Cryptography - Symbol-pair codes are proposed to protect against pair-errors in symbol-pair read channels. The research of symbol-pair codes with the largest possible minimum... 相似文献
12.
Cyclic code is an interesting topic in coding theory and communication systems. In this paper, we investigate the ternary cyclic codes with parameters based on some results proposed by Ding and Helleseth in 2013. Six new classes of optimal ternary cyclic codes are presented by determining the solutions of certain equations over . 相似文献
13.
In this paper, by analyzing the solutions of certain equations over , we present four classes of optimal ternary cyclic codes with parameters . It is shown that some recent work on this class of optimal ternary cyclic codes are special cases of our results. 相似文献
14.
Edward Spence
Vladimir D. Tonchev
《Discrete Mathematics》1992,110(1-3):265-268A method is given for constructing extremal binary self-dual [42, 21, 8]-codes from certain symmetric 2-(41, 16, 6) designs. 相似文献
15.
Naoyuki Horiguchi Tsuyoshi Miezaki Hiroyuki Nakasora 《Designs, Codes and Cryptography》2014,72(3):529-537
Let \(D\) be the support design of the minimum weight of an extremal binary doubly even self-dual \([24m,12m,4m+4]\) code. In this note, we consider the case when \(D\) becomes a \(t\) -design with \(t \ge 6\) . 相似文献
16.
17.
In this article we introduce a method of constructing binary linear codes and computing their weights by means of Boolean functions arising from mathematical objects called simplicial complexes. Inspired by Adamaszek (Am Math Mon 122:367–370, 2015) we introduce n-variable generating functions associated with simplicial complexes and derive explicit formulae. Applying the construction (Carlet in Finite Field Appl 13:121–135, 2007; Wadayama in Des Codes Cryptogr 23:23–33, 2001) of binary linear codes to Boolean functions arising from simplicial complexes, we obtain a class of optimal linear codes and a class of minimal linear codes. 相似文献
18.
In this paper, we present examples of codes all of whose weight classes support 1‐designs, with duals whose classes include two that support 2‐designs. We can find these examples in the triply even binary codes of length 48, which have been classified by Betsumiya and Munemasa. 相似文献
19.
A cyclic code is a -ary cyclic code of length , minimum Hamming distance and weight . In this paper, we investigate cyclic codes. A new upper bound on , the largest possible number of codewords in a cyclic code, is given. Two new constructions for optimal cyclic codes based on cyclic difference packings are presented. As a consequence, the exact value of is determined for any positive integer . We also obtain some other infinite classes of optimal cyclic codes. 相似文献
20.
An (n,M,d;q) code is called equidistant code if the Hamming distance between any two codewords is d. It was proved that for any equidistant (n,M,d;q) code, d?nM(q-1)/(M-1)q(=dopt, say). A necessary condition for the existence of an optimal equidistant code is that dopt be an integer. If dopt is not an integer, i.e. the equidistant code is not optimal, then the code with d=⌊dopt⌋ is called good equidistant code, which is obviously the best possible one among equidistant codes with parameters n,M and q. In this paper, some constructions of good equidistant codes from balanced arrays and nested BIB designs are described. 相似文献