Quantum code construction from two classical codes $D_1[n,k_1,d_1]$ and $D_2[n,k_2,d_2]$ over the field $\mathbb {F}_{p^m}$ ( $p$ is prime $m$ an integer) satisfying dual containing criteria $D_1^{\perp } \subset D_2$ using Calderbank–Shor–Steane (CSS) framework well-studied. We show that generalization of CSS for qubits to qudits yields different classes codes, namely, {F}_{p}$ -linear well-kn...

Optimal linear codes and constant-weight codes play very important roles in coding theory and have attached a lot of attention. In this paper, we mainly present some optimal linear codes and some optimal constant-weight codes derived from the linear codes. Firstly, we give a construction of linear codes from trace and norm functions. In some cases, its weight distribution is completely determin...

Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...

One of the main challenges of coding theory is to construct linear codes with the best possible parameters. Various algebraic and combinatorial methods along with computer searches are used to construct codes with better parameters. Given the computational complexity of determining the minimum distance of a code, exhaustive searches are not feasible for all but small parameter sets. Therefore, ...

Let $\mathbb{F}_{p^m}$ be a finite field with $p^m$ elements, where $p$ is an odd prime and $m$ positive integer. Recently, \cite{Hengar} \cite{Wang2020} determined the weight distributions of subfield codes form $$\mathcal{C}_f=\left\{\left(\left( {\rm Tr}_1^m(a f(x)+bx)+c\right)_{x \in \mathbb{F}_{p^m}}, Tr}_1^m(a)\right)\, : \, a,b \mathbb{F}_{p^m}, c \mathbb{F}_p\right\}$$ for $f(x)=x^2$ ...

Let Fq be a finite field with q elements and denote by θ : Fq → Fq an automorphism of Fq. In this paper, we deal with linear codes of Fnq invariant under a semi-linear map T : F q → F q for some n ≥ 2. In particular, we study three kind of their dual codes, some relations between them and we focus on codes which are products of module skew codes in the non-commutative polynomial ring as a subca...

In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.