Related papers: Low-weight codewords in cyclic codes
A code is said to be two-weight if the non-zero codewords have only two different a weight w1 and w2. Two-weight codes are closely related to strongly regular graphs. In this paper. It is shown that a consta-cyclic code of composite length…
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…
The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and…
In this letter, we introduce an efficient method for estimating weight distributions of polar codes and polarization-adjusted convolutional (PAC) codes. Based on a recursive algorithm of computing the weight enumerating functions of polar…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
The interplay between coding theory and $t$-designs has attracted a lot of attention for both directions. It is well known that the supports of all codewords with a fixed weight in a code may hold a $t$-design. In this paper, by determining…
As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight…
The cyclic codes with parity check polynomial the reciprocal of the characteristic polynomial of the Fibonacci recurrence over a prime finite field are shown to have either one weight or two weights. When these codes are irreducible cyclic…
Let $q=2^n$, $0\leq k\leq n-1$, $n/\gcd(n,k)$ be odd and $k\neq n/3, 2n/3$. In this paper the value distribution of following exponential sums \[\sum\limits_{x\in \bF_q}(-1)^{\mathrm{Tr}_1^n(\alpha x^{2^{2k}+1}+\beta x^{2^k+1}+\ga…
We consider cyclic codes $\mathcal{C}_\mathcal{L}$ associated to quadratic trace forms in $m$ variables $Q_R(x) = \operatorname{Tr}_{q^m/q}(xR(x))$ determined by a family $\mathcal{L}$ of $q$-linearized polynomials $R$ over…
In this paper, a family of reducible cyclic codes over GF(p) whose duals have four zeros is presented, where p is an odd prime. Furthermore, the weight distribution of these cyclic codes is determined.
We present novel decoding schemes for hard and soft decision decoding of block codes using the minimal weight codewords of the dual code. The decoding schemes will be described for cyclic codes where polynomials can be used, however, the…
A cyclic codes of length $n$ over the rings $Z_{2^{m}}$ of integer of modulo $2^{m}$ is a linear code with property that if the codeword $(c_0,c_1,...,c_{n-1})\in \mathcal{C}$ then the cyclic shift $(c_1,c_2,...,c_0)\in \mathcal{C}$.…
We present a framework for minimizing costs in constant weight codes while maintaining a certain amount of differentiable codewords. Our calculations are based on a combinatorial view of constant weight codes and relay on simple…
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. Most previous results obtained so far were for cyclic codes with no more than three zeroes. Inspired by the works…
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 the past few years, linear codes with few weights and their weight analysis have been widely studied. In this paper, we further investigate a class of two-weight or three-weight linear codes from defining sets and determine their weight…
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…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…
A binary linear code $C$ is a $\mathbb{Z}_2$-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be…