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A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…
Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes…
We study the performance of ternary isodual codes which are not self-dual and ternary self-dual codes, as measured by the decoding error probability in bounded distance decoding. We compare the performance of ternary double circulant and…
A relationship between $s$-extremal singly even self-dual $[24k+8,12k+4,4k+2]$ codes and extremal doubly even self-dual $[24k+8,12k+4,4k+4]$ codes with covering radius meeting the Delsarte bound, is established. As an example of the…
In this paper we construct binary self-dual codes using the \'etale cohomology of $\mathbb{Z}/2$ on the spectra of rings of $S$-integers of global fields. We will show that up to equivalence, all self-dual codes of length at least 4 arise…
The concept of group divisible codes, a generalization of group divisible designs with constant block size, is introduced in this paper. This new class of codes is shown to be useful in recursive constructions for constant-weight and…
Binary self-dual codes with large minimum distances, such as the extended Hamming code and the Golay code, are fascinating objects in the coding theory. They are closely related to sporadic simple groups, lattices and invariant theory. A…
This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic $p^2$ and order $p^4$ with $p$ and odd prime. When $p \equiv 3 \pmod{4},$ we give…
Generalized Bicycle (GB) codes offer a compelling alternative to surface codes for quantum error correction. This paper focuses on (2,2)-Generalized Bicycle codes, constructed from pairs of binary circulant matrices with two non-zero…
The ring in the title is the first non commutative ring to have been used as alphabet for block codes. The original motivation was the construction of some quaternionic modular lattices from codes. The new application is the construction of…
The rings $Z_{4}+\nu Z_{4}$ have been classified into chain rings and non-chain rings on the basis of the values of $\nu^{2} \in Z_{4}+\nu Z_{4}.$ In this paper, the structure of cyclic codes of arbitrary length over the rings $Z_{4}+\nu…
Given a finite group $G$ and an extension of finite chain rings $S|R$, one can consider the group rings $\mathscr{S} = S[G]$ and $\mathscr{R} = R[G]$. The group ring $\mathscr{S}$ can be viewed as an $R$-bimodule, and any of its…
In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodular lattices in dimension 40 are studied. We give a classification of extremal singly even self-dual codes of length 40. We also give a…
We give restrictions on the weight enumerators of ternary near-extremal self-dual codes of length divisible by $12$ and quaternary near-extremal Hermitian self-dual codes of length divisible by $6$. We consider the weight enumerators for…
We show that there are good long binary generalized quasi-cyclic self-dual (either Type I or Type II) codes.
This paper presents four new classes of binary quantum codes with minimum dis- tance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the…
In this paper quadratic residue codes over the ring Fp + vFp are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes share similar properties with quadratic residue…
In this paper, we determine all self-dual codes over $F_p+vF_p$ ($v^2=v$) in terms of self-dual codes over the finite field $F_p$ and give an explicit construction for self-dual codes over $F_p+vF_p$, where $p$ is a prime.
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…