Related papers: Weight Structure of Low/High-Rate Polar Codes and …
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…
In this paper, we present a deterministic algorithm to count the low-weight codewords of punctured and shortened pure and pre-transformed polar codes. The method first evaluates the weight properties of punctured/shortened polar cosets.…
Linear codes with few weights have many applications in secret sharing schemes, authentication codes, communication and strongly regular graphs. In this paper, we consider linear codes with three weights in arbitrary characteristic. To do…
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this…
The weight distribution and weight hierarchy of linear codes are two important research topics in coding theory. In this paper, by choosing proper defining sets from inhomogeneous quadratic functions over $\mathbb{F}_{q}^{2},$ we construct…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
Reed Muller (RM) codes are known for their good minimum distance. One can use their structure to construct polar-like codes with good distance properties by choosing the information set as the rows of the polarization matrix with the…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error…
In this work, we present a deterministic algorithm for computing the entire weight distribution of polar codes. As the first step, we derive an efficient recursive procedure to compute the weight distribution that arises in successive…
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…
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…
The weight distribution and weight hierarchy of a linear code are two important research topics in coding theory. In this paper, choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}:…
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…
Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, some kinds of p-ary linear codes with few weights are constructed by use of the given de ning set,…
Boolean functions can be used to construct binary linear codes in many ways, and vice versa. The objective of this short article is to point out a connection between the weight distributions of all projective binary linear codes and the…
This paper is concerned with the affine-invariant ternary codes which are defined by Hermitian functions. We compute the incidence matrices of 2-designs that are supported by the minimum weight codewords of these ternary codes. The linear…
It is well-known that few-weight linear codes have better applications in secret sharing schemes \cite{JY2006,CC2005}.In particular, projective two-weight codes are very precious as they are closely related to finite projective spaces,…
In this paper, we have introduced the concepts of support distribution and the support enumerator as refinements of the classical weight distribution and weight enumerator respectively, capturing coordinate level activity in linear block…
Linear codes have been an interesting subject of study for many years. Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, a class of three-weight linear codes over Fp…