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Cyclic codes over F2 × (F2 + vF2) and binary quantum codes

Fatma Çalışkan, Refia Aksoy

Published Jan 1, 2023• 1 citation
Publisher

Abstract

In the present study, we define cyclic codes over the commutative principal ideal ring F2 ? (F2 + vF2) with v2 = v and obtain some results on cyclic codes over F2 ? (F2 + vF2). We also investigate the dual of a cyclic code over F2 ? (F2 + vF2) depending on two inner products. We determine a generator polynomial of cyclic codes and give the calculation of the number of cyclic codes over F2 ? (F2 + vF2). Furthermore, we show that the Gray images of a cyclic code over F2 ? (F2 + vF2) of length n are binary quasi-cyclic codes of length 3n and of index 3. We find numerous binary codes as Gray images of cyclic codes over F2 ? (F2 + vF2) and tabulate the optimal ones. Moreover, we show that it is possible to obtain binary quantum error-correcting codes (QECCs) from cyclic codes over F2 ? (F2 + vF2).

DOI
10.2298/fil2315137c

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