# Journal of the Ramanujan Mathematical Society

Volume 37, Issue 1, March 2022 pp. 49–61.

t-Frobenius Negacyclic codes

**Authors**:
Priyabrata Bag and Santanu Dey

**Author institution:**School of Mathematical Sciences, Narsee Monjee Institute of Management Studies, Vile Parle (W), Mumbai, Maharashtra 400056, India

**Summary: **
Let F{p} denote the finite field of order p, where p is an odd prime. We study
certain quantum negacyclic codes over F{p} which we call t-Frobenius negacyclic
codes. We obtain a criterion for constructing such codes from certain subspaces
of F{n}{p} × F{n}{p} 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.

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