Additive codes received much attention due to their connections with quantum codes. On the other hand, skew cyclic codes proved to be a useful class of codes that contain many good codes. In this work, we introduce and study additive skew cyclic codes over the quaternary field [Formula: see text], obtaining some structural properties of these codes. Moreover, we also show that many best known and optimal quantum codes can be obtained from this class.

Discrete Mathematics Algorithms and ApplicationsMar 30, 201614 citations

(f, σ, δ)-skew Polycyclic Codes and Their Applications to Quantum Codes

Shikha Patel, Habibul Islam, Om Prakash

International Journal of Theoretical PhysicsFeb 1, 20225 citations

Discrete Mathematics

A class of skew cyclic codes and application in quantum codes construction

Hai Quang Dinh, Tushar Bag, Ashish Kumar Upadhyay, Ramakrishna Bandi, Roengchai Tansuchat

Published Oct 20, 2020• 19 citations

Publisher

DOI: 10.1016/j.disc.2020.112189

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{\mathbb {F}}_qR

-linear skew constacyclic codes and their application of constructing quantum codes

\mathbb{F}_q\mathcal{R}

-skew cyclic codes and their application to quantum codes

Let

p

be a prime and

\mathbb{F}_q

be the finite field of order

q=p^m

. In this paper, we study

\mathbb{F}_q\mathcal{R}

-skew cyclic codes where

\mathcal{R}=\mathbb{F}_q+u\mathbb{F}_q

with

u^2=u

. To characterize

\mathbb{F}_q\mathcal{R}

-skew cyclic codes, we first establish their algebraic structure and then discuss the dual-containing properties by considering a non-degenerate inner product. Further, we define a Gray map over

\mathbb{F}_q\mathcal{R}

and obtain their

\mathbb{F}_q

-Gray images. As an application, we apply the CSS (Calderbank-Shor-Steane) construction on Gray images of dual containing

\mathbb{F}_q\mathcal{R}

-skew cyclic codes and obtain many quantum codes with better parameters than the best-known codes available in the literature.