Related papers: Higher weight distribution of linearized Reed-Solo…
In this work, doubly extended linearized Reed--Solomon codes and triply extended Reed--Solomon codes are generalized. We obtain a general result in which we characterize when a multiply extended code for a general metric attains the…
Determining the weight distributions of the projective Reed-Muller codes is a very hard problem and has been studied extensively in the literature. In this article, we provide an alternative proof of the second weight of the projective…
We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of…
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…
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…
Irreducible cyclic codes are an interesting type of codes and have applications in space communications. They have been studied for decades and a lot of progress has been made. The objectives of this paper are to survey and extend earlier…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…
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 note, we reveal a relation between the weight distribution of a concatenated code ensemble based on the Plotkin construction and those of its component codes. The relation may find applications in the calculation of the ensemble…
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…
Given a constant weight linear code, we investigate its weight hierarchy and the Stanley-Reisner resolution of its associated matroid regarded as a simplicial complex. We also exhibit conditions on the higher weights sufficient to conclude…
Cyclic codes have been widely used in digital communication systems and consume electronics as they have efficient encoding and decoding algorithms. The weight distribution of cyclic codes has been an important topic of study for many…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
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 address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…
The new method for Reed-Solomon codes decoding is introduced. The method is based on the star trellis decoding of the binary image of Reed-Solomon codes.
We determine the higher weight spectra of $q$-ary Reed-Muller codes $C_q=RM_q(2,2)$ for all prime powers $q$. This is equivalent to finding the usual weight distributions of all extension codes of $C_q$ over every field extension of $F_q$…
In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from…
We give a description of the duals of linearized Reed-Solomon codes in terms of codes obtained by taking residues of Ore rational functions. Our construction shows in particular that, under some assumptions on the base field, the class of…
This paper investigates the relation between linear codes and the stabilizer in ${\rm GL}_2(\mathbb{C})$ of their weight enumerators. We prove a result on the finiteness of stabilizers and give a complete classification of linear codes with…