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Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight Griesmer $[\frac{q^k-1}{q-1},k…
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
We introduce Berman-intersection-dual Berman (BiD) codes. These are abelian codes of length $3^m$ that can be constructed using Kronecker products of a $3 \times 3$ kernel matrix. BiD codes offer minimum distance close to that of…
We construct a family of linear maximally recoverable codes with locality $r$ and dimension $r+1.$ For codes of length $n$ with $r\approx n^\alpha, 0\le\alpha\le 1$ the code alphabet is of the order $n^{1+3\alpha},$ which improves upon the…
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
Using the notion of generalized weight we improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes.
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of…
Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun {\em et al}. Inspired by their work, we present two new constructions of codes over the ring $\Bbb F_2+u\Bbb F_2$…
Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…
Based on a generic construction, two classes of ternary three-weight linear codes are obtained from a family of power functions, including some APN power functions. The weight distributions of these linear codes are determined through…
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…
Binary constant weight codes have important applications and have been studied for many years. Optimal or near-optimal binary constant weight codes of small lengths have been determined. In this paper we propose a new construction of…
There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds…
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide…
A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…
The construction of deletion codes for the Levenshtein metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of translates of…
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…