相关论文: The $b$-weight distribution for MDS codes
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…
Using techniques and results from Kudekar et al. we strengthen the bounds on the weight distribution of linear codes achieving capacity on the BEC, which were shown by the first author. In particular, we show that for any doubly transitive…
The size of the Hamming distance spectrum of a code has received great attention in recent research. The main objective of this paper is to extend these significant theories to the $b$-symbol distance spectrum. We examine this question for…
This paper develops an algorithmic approach for obtaining approximate, numerical estimates of the sizes of subcodes of Reed-Muller (RM) codes, all of the codewords in which satisfy a given constraint. Our algorithm is based on a statistical…
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…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
The duals of cyclic codes with two zeros have been extensively studied, and their weight distributions have recently been evaluated in some cases. In this note, we determine the weight distribution of a certain new class of such codes by…
MDS self-dual codes have nice algebraic structures and are uniquely determined by lengths. Recently, the construction of MDS self-dual codes of new lengths has become an important and hot issue in coding theory. In this paper, we develop…
Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. MDS symbol-pair codes are…
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…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Cyclic codes have been studied for many years, but their weight…
The bilateral minimum distance of a binary linear code is the maximum $d$ such that all nonzero codewords have weights between $d$ and $n-d$. Let $Q\subset \{0,1\}^n$ be a binary linear code whose dual has bilateral minimum distance at…
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.…
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…
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said…
The symbol-pair codes over finite fields have been raised for symbol-pair read channels and motivated by application of high-density data storage technologies [1, 2]. Their generalization is the code for b-symbol read channels (b > 2). Many…
The error-correcting pair is a general algebraic decoding method for linear codes. The near maximal distance separable (NMDS) linear code is a subclass of linear codes and has applications in secret sharing scheme and communication systems…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special…
This paper investigates the relationship between the rank weight distribution of a linear code and that of its dual code. The main result of this paper is that, similar to the MacWilliams identity for the Hamming metric, the rank weight…
Motivated by comparative genomics, Chen et al. [9] introduced the Maximum Duo-preservation String Mapping (MDSM) problem in which we are given two strings $s_1$ and $s_2$ from the same alphabet and the goal is to find a mapping $\pi$…