Related papers: Maximum weight spectrum codes with reduced length
We give an upper bound that relates the minimum weight of a nonzero componentwise product of codewords from some given number of linear codes, with the dimensions of these codes. Its shape is a direct generalization of the classical…
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
Sum-rank-metric codes have wide applications in universal error correction, multishot network coding, space-time coding and the construction of partial-MDS codes for repair in distributed storage. Fundamental properties of sum-rank-metric…
A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code…
A linear code over $\mathbb{F}_q$ with the Hamming metric is called $\Delta$-divisible if the weights of all codewords are divisible by $\Delta$. They have been introduced by Harold Ward a few decades ago. Applications include subspace…
The maximum size of a binary code is studied as a function of its length N, minimum distance D, and minimum codeword weight W. This function B(N,D,W) is first characterized in terms of its exponential growth rate in the limit as N tends to…
The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes…
In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…
A binary code of blocklength $n$ and codebook size $M$ is called an $(n,M)$ code, which is studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood (ML) decoding. For any $n \geq 2$, some optimal codes among the…
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary…
The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension $2$. In this paper, we give some conditions for the nonexistence of quaternary Hermitian linear complementary dual codes with…
The singleton defect of an $[n,k,d]$ linear code ${\cal C}$ is defined as $s({\cal C})=n-k+1-d$. Codes with $S({\cal C})=0$ are called maximum distance separable (MDS) codes, and codes with $S(\cal C)=S(\cal C ^{\bot})=1$ are called near…
In this paper, based on the theory of defining sets, a class of four-weight or five-weight linear codes over Fp is constructed. The complete weight enumerators of the linear codes are determined by means of Weil sums. In some case, there is…
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…
In this paper, we completely determine the number of solutions to $ \operatorname{Tr}^{q^2}_q(bx+b)+c=0, x\in \mu_{q+1}\backslash \{-1\}$ for all $b\in \mathbb{F}_{q^2}, c\in\mathbb{F}_{q}$. As an application, we can give the weight…
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…
A Gray code is a listing structure for a set of combinatorial objects such that some consistent (usually minimal) change property is maintained throughout adjacent elements in the list. While Gray codes for m-ary strings have been…
One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) =…
Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive…
Constructions of quantum MDS codes have been studied by many authors. We refer to the table in page 1482 of [3] for known constructions. However there are only few $q$-ary quantum MDS $[[n,n-2d+2,d]]_q$ codes with minimum distances…