$t$-Frobenius Negacyclic Codes

Abstract

Let ${\mathbb{F}}_p$ denote the finite field of order $p$, where $p$ is an odd prime. We study certain quantum negacyclic codes over ${\mathbb{F}}_p$ which we call $t$-Frobenius negacyclic codes. We obtain a criterion for constructing such codes from certain subspaces of ${\mathbb{F}}_p^n\times {\mathbb{F}}_p^n$ in terms of generating pairs of ideals of cyclotomic rings and we completely classify all linear $t$-Frobenius negacyclic codes. Further, the notion of BCH distance is extended for these codes and several new codes are identified.

15 pages

References in corpus (2)

• Good Quantum Error-Correcting Codes Exist
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound