TY - JOUR
AU - Ali, Shakir
AU - Sharma, Pushpendra
PY - 2024/08/21
Y2 - 2024/10/10
TI - ON QUANTUM CODES CONSTRUCTION FROM CONSTACYCLIC CODES OVER THE RING I_q[u,v] /
JF - Journal of the Indonesian Mathematical Society
JA - JIMS
VL - 30
IS - 2
SE - Articles
DO - 10.22342/jims.30.2.1587.139-159
UR - http://jims-a.org/index.php/jimsa/article/view/1587
SP - 139-159
AB - <p>This paper focuses on studying the properties of constacyclic codes, quantum error-correcting codes. The code is studied over a specific mathematical structure called the ring $\mathfrak{S}$, which is defined as $\mathfrak{S}=\mathfrak{I}_q[\mathfrak{u},\mathfrak{v}]/\langle \mathfrak{u}^2-\alpha^2,~ \mathfrak{v}^2-\alpha^2,~\mathfrak{u}\mathfrak{v}-\mathfrak{v}\mathfrak{u} \rangle$, where $\mathfrak{I}_q$ is a finite field of $q$ elements, $\alpha$ be the nonzero elements of the field $\mathfrak{I}_q$ and $q$ is a power of an odd prime $p$ such that $q=p^m, ~\textup{for}~ m \ge 1$. The paper also introduces a Gray map and use it to decompose constacyclic codes over the ring $\mathfrak{S}$ into a direct sum of constacyclic codes over $\mathfrak{I}_q$. We construct new and better quantum error-correcting codes over the ring $\mathfrak{S}$ (cf.; Table 1 and Table 2). Moreover, we also obtain best known linear codes as well as best dimension linear codes (cf.; Table 4).</p>
ER -