Related papers: Ternary primitive LCD BCH codes
Our main technical result is that, in the coset leader graph of a linear binary code of block length n, the metric balls spanned by constant-weight vectors grow exponentially slower than those in $\{0,1\}^n$. Following the approach of…
In this paper, we construct three ternary linear codes associated with the orthogonal group O^-(2,q) and the special orthogonal groups SO^-(2,q) and SO^-(4,q). Here q is a power of three. Then we obtain recursive formulas for the power…
Discovered by Bose, Chaudhuri and Hocquenghem, the BCH family of error correcting codes are one of the most studied families in coding theory. They are also among the best performing codes, particularly when the number of errors being…
Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and…
Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in $\ell_1$-metric. By using packings and group divisible designs in combinatorial design theory, we give…
We study the distribution of the number of rational points in a family of curves over a finite field of characteristic 2. This distribution determines the coset weight distribution of a certain BCH code.
In this paper non-trivial non-linear binary systematic AMDS codes are classified in terms of their weight distributions, employing only elementary techniques. In particular, we show that their length and minimum distance completely…
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their…
Tang and Ding [IEEE IT 67 (2021) 244-254] studied the class of narrow-sense BCH codes $\mathcal{C}_{(q,q+1,4,1)}$ and their dual codes with $q=2^m$ and established that the codewords of the minimum (or the second minimum) weight in these…
Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and…
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
We define and study burst-covering codes. We provide some general bounds connecting the parameters of a code with its burst-covering radius. We then provide stronger bounds on the burst-covering radius of cyclic codes, by employing…
It is well known that the problem of determining the weight distributions of families of cyclic codes is, in general, notoriously difficult. An even harder problem is to find characterizations of families of cyclic codes in terms of their…
Linear codes have been an interesting subject of study for many years. Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, a class of three-weight linear codes over Fp…
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…
BCH codes form an important class of cyclic codes, which have applications in communication and data storage systems. Although the BCH bound provides a lower bound on the minimum distance of BCH codes, determining the true minimum distances…
Ternary self-dual codes have been classified for lengths up to 20. At length 24, a classification of only extremal self-dual codes is known. In this paper, we give a complete classification of ternary self-dual codes of length 24 using the…
The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. A subclass of attractive BCH codes is the…
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary…