Related papers: A Class of Three-Weight Linear Codes and Their Com…
We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code.…
In this paper, we construct a large family of projective linear codes over ${\mathbb F}_{q}$ from the general simplicial complexes of ${\mathbb F}_{q}^m$ via the defining-set construction, which generalizes the results of [IEEE Trans. Inf.…
We consider a class of linear codes associated to projective algebraic varieties defined by the vanishing of minors of a fixed size of a generic matrix. It is seen that the resulting code has only a small number of distinct weights. The…
We construct strongly walk-regular graphs as coset graphs of the duals of codes with three non-zero homogeneous weights over $\mathbb{Z}_{p^m},$ for $p$ a prime, and more generally over chain rings of depth $m$, and with a residue field of…
We classify all $q$-ary $\Delta$-divisible linear codes which are spanned by codewords of weight $\Delta$. The basic building blocks are the simplex codes, and for $q=2$ additionally the first order Reed-Muller codes and the parity check…
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…
Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun {\em et al.} We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to…
In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given $p,\epsilon>0$, we study (i) The $p$-bounded constraint: a binary vector of size $m$ is said to be $p$-bounded if its weight is at most…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
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…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
In this paper, a family of five-weight reducible cyclic codes is presented. Furthermore, the weight distribution of these cyclic codes is determined, which follows from the determination of value distributions of certain exponential sums.
In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…
In this paper we present a fast and efficient method to find partial weight enumerator (PWE) for binary linear block codes by using the error impulse technique and Monte Carlo method. This PWE can be used to compute an upper bound of the…
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…
The generalized Hamming weights (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we…
In this paper, we first generalize the class of linear codes by Ding and Ding (IEEE TIT, 61(11), pp. 5835-5842, 2015). Then we mainly study the augmented codes of this generalized class of linear codes. For one thing, we use Gaussian sums…