Geodesic
Cyclic codes over fF2 × (F 2 + vF2 ) and binary quantum codes
Filomat, Tome 37 (2023) no. 15, p. 5137

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DOI

In the present study, we define cyclic codes over the commutative principal ideal ring F 2 × (F 2 + vF 2) with v 2 = v and obtain some results on cyclic codes over F 2 × (F 2 + vF 2). We also investigate the dual of a cyclic code over F 2 × (F 2 + vF 2) depending on two inner products. We determine a generator polynomial of cyclic codes and give the calculation of the number of cyclic codes over F 2 × (F 2 + vF 2). Furthermore, we show that the Gray images of a cyclic code over F 2 × (F 2 + vF 2) 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 F 2 × (F 2 + vF 2) and tabulate the optimal ones. Moreover, we show that it is possible to obtain binary quantum error-correcting codes (QECCs) from cyclic codes over F 2 × (F 2 + vF 2).
DOI : 10.2298/FIL2315137C
Classification : 94B15, 11T71, 94B60
Keywords: Cyclic code, Generator polynomial, Dual code, Quantum code 
Fatma Çalişkan; Refia Aksoy. Cyclic codes over fF2 × (F 2 + vF2 ) and binary quantum codes. Filomat, Tome 37 (2023) no. 15, p. 5137 . doi: 10.2298/FIL2315137C
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     author = {Fatma \c{C}ali\c{s}kan and Refia Aksoy},
     title = {Cyclic codes over {fF2} {\texttimes} {(F} 2 + {vF2} ) and binary quantum codes},
     journal = {Filomat},
     pages = {5137 },
     year = {2023},
     volume = {37},
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     doi = {10.2298/FIL2315137C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2315137C/}
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