Related papers: Classification of binary systematic codes of small…
In this paper, the 3-rank of the incidence matrices of 2-designs supported by the minimum weight codewords in a family of ternary linear codes considered in [C. Ding, C. Li, Infinite families of 2-designs and 3-designs from linear codes,…
Cyclic codes have attracted a lot of research interest for decades as they have efficient encoding and decoding algorithms. In this paper, for an odd prime $p$, the weight distributions of two classes of $p$-ary cyclic codes are completely…
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for…
We classify binary minimal clones into seven categories: affine algebras, rectangular bands, $p$-cyclic groupoids, spirals, non-Taylor partial semilattices, melds, and dispersive algebras. Each category has nice enough properties to…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
In this paper, for an even integer $n\geq 4$ and any positive integer $k$ with ${\rm gcd}(n/2,k)={\rm gcd}(n/2-k,2k)=d$ being odd, a class of $p$-ary codes $\mathcal{C}^k$ is defined and their weight distribution is completely determined,…
The structure of a linear block code is pivotal in defining fundamental properties, particularly weight distribution, and code design. In this study, we characterize the Type II structure of polar codewords with weights less than twice the…
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with…
In this paper, we study the weight spectrum of linear codes with \emph{super-linear} field size and use the probabilistic method to show that for nearly all such codes, the corresponding weight spectrum is very close to that of a maximum…
In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined.
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…
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we…
It has been known since the 1970's that the difference of the non-zero weights of a projective $\mathbb{F}_q$-linear two-weight has to be a power of the characteristic of the underlying field. Here we study non-projective two-weight codes…
This paper is concerned with the affine-invariant ternary codes which are defined by Hermitian functions. We compute the incidence matrices of 2-designs that are supported by the minimum weight codewords of these ternary codes. The linear…
Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their…
In this paper, based on the theory of defining sets, two classes of five-weight or six-weight linear codes over Fp are constructed. The weight distributions of the linear codes are determined by means of Weil sums and a new type of…
Asymptotic concentration behaviors of linear combinations of weight distributions on the random linear code ensemble are presented. Many important properties of a binary linear code can be expressed as the form of a linear combination of…
The study of linear codes over a finite field of odd cardinality, derived from determinantal varieties obtained from symmetric matrices of bounded rank, was initiated in a recent paper by the authors. There, one found the minimum distance…