Related papers: Classification of binary systematic codes of small…
Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of $q$-ary linear codes under some certain conditions, where $q$ is a power…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
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…
An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.
We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…
In this paper, we study the relationship between algebraic manipulation detection (AMD) codes and highly nonlinear functions. As applications, on one hand, a generic construction for systematic AMD codes is introduced based on highly…
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide…
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…
The average weight distribution of a regular low-density parity-check (LDPC) code ensemble over a finite field is thoroughly analyzed. In particular, a precise asymptotic approximation of the average weight distribution is derived for the…
We consider weighted Reed-Muller codes over point ensemble $S_1 \times...\times S_m$ where $S_i$ needs not be of the same size as $S_j$. For $m = 2$ we determine optimal weights and analyze in detail what is the impact of the ratio…
It is well known that the problem of determining the weight distributions of families of cyclic codes is, in general, notoriously difficult. An even harder problem is to find characterizations of families of cyclic codes in terms of their…
Detailed information about the weight distribution of a convolutional code is given by the adjacency matrix of the state diagram associated with a controller canonical form of the code. We will show that this matrix is an invariant of the…
Irreducible cyclic codes are one of the largest known classes of block codes which have been investigated for a long time. However, their weight distributions are known only for a few cases. In this paper, a class of irreducible cyclic…
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…
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…
We consider a bound on the bias reduction of a random number generator by processing based on binary linear codes. We introduce a new bound on the total variation distance of the processed output based on the weight distribution of the code…
We use a simple construction called `recursive subproducts' (that is known to yield good codes of lengths $n^m$, $n \geq 3$) to identify a family of codes sandwiched between first-order and second-order Reed-Muller (RM) codes. These codes…
The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that…