Related papers: Weight distributions of cyclic codes with respect …
In this paper, we investigate the symbol-pair weight distributions of MDS codes and simplex codes over finite fields. Furthermore, the result shows that all the nonzero codewords of simplex codes have the same symbol $b$-weight and…
In this paper, we construct an infinite family of five-weight codes from trace codes over the ring $R=\mathbb{F}_2+u\mathbb{F}_2$, where $u^2=0.$ The trace codes have the algebraic structure of abelian codes. Their Lee weight is computed by…
Let $R$ be a finite commutative chain ring with unique maximal ideal $\langle \gamma\rangle$, and let $n$ be a positive integer coprime with the characteristic of $R/\langle \gamma\rangle$. In this paper, the algebraic structure of cyclic…
In this manuscript, we construct a class of projective three-weight linear codes and two classes of projective four-weight linear codes over F2 from the defining sets construction, and determine their weight distributions by using additive…
Given the finite field $\mathbb{F}_{q}$, for a prime power $q$, in this paper we present a way of constructing spreads of $\mathbb{F}_{q}^{n}$. They will arise as orbits under the action of an Abelian non-cyclic group. First, we construct a…
A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.
Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This…
Combinatorial $t$-designs have been an important research subject for many years, as they have wide applications in coding theory, cryptography, communications and statistics. The interplay between coding theory and $t$-designs has been…
Let $q=p^n$ with $n=2m$ and $p$ be an odd prime. Let $0\leq k\leq n-1$ and $k\neq m$. In this paper we determine the value distribution of following exponential(character) sums \[\sum\limits_{x\in \bF_q}\zeta_p^{\Tra_1^m (\alpha…
Let $n\geq 3$ be a positive integer and let $\mathbb{F}_{q^k}$ be the splitting field of $x^n-1$. By $\gamma$ we denote a primitive element of $\mathbb{F}_{q^k}$. Let $C$ be a cyclic code of length $n$ whose check polynomial contains two…
The weight hierarchy of a linear code has been an important research topic in coding theory since Wei's original work in 1991. Choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}: f(x)+g(y)=0\Big\}$…
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.…
{A cyclic subspace code is a union of the orbits of subspaces contained in it. In a recent paper, Gluesing-Luerssen et al. (Des. Codes Cryptogr. 89, 447-470, 2021) showed that the study of the distance distribution of a single orbit cyclic…
In this paper we consider the problem of determining the weight spectrum of q-ary codes C(3,m) associated with Grassmann varieties G(3,m). For m=6 this was done by Nogin. We derive a formula for the weight of a codeword of C(3,m), in terms…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
We study q-ary linear codes C obtained from Veronese surfaces over finite fields. We show how one can find the higher weight spectra of these codes, or equivalently, the weight distribution of all extension codes of C over all field…
A linear code $C$ over $\mathbb{F}_q$ is called $\Delta$-divisible if the Hamming weights $\operatorname{wt}(c)$ of all codewords $c \in C$ are divisible by $\Delta$. The possible effective lengths of $q^r$-divisible codes have been…
Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…
We calculate exact values of the decycling numbers of $C_{m} \times C_{n}$ for $m=3,4$, of $C_{n}^{2}$, and of $C_{n}^{3}$.
The weight distribution of the binary self-dual $[128,64]$ code being the extended code $C^{*}$ of the code $C$ spanned by the incidence vectors of the blocks of the polarity design in $PG(6,2)$ [11] is computed. It is shown also that…