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Let $p$ be an odd prime. The algebraic structure of all negacyclic codes of length $8p^s$ over the finite commutative chain ring $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ where $u^2=0$ is studied in this paper. Moreover, we classify all negacyclic codes of length $8p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ into 5 cases, i.e., $p^m\equiv 1 \pmod{16}$, $p^m\equiv 3,11 \pmod{16}$, $p^m\equiv 5,13 \pmod{16}$, $p^m\equiv 7,15 \pmod{16}$ and $p^m\equiv 9 \pmod{16}$. From that, the structures of dual and some self-dual negacyclic codes and number of codewords of negacyclic codes are obtained.
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참고문헌 (19)
참고문헌 신청
Taher Abualrub / 2009 / Constacyclic codes over / Journal of the Franklin Institute 346(5):520~529
G. Castagnoli / 1991 / On repeated-root cyclic codes / IEEE Transactions on Information Theory 37(2):337~342
B. Chen / 2016 / Constacyclic codes of length 2ps over Fpm + uFpm / Finite Fields Appl. 37:108~130
H.Q. Dinh / 2005 / Negacyclic Codes of Length<tex>$2^s$</tex>Over Galois Rings / IEEE Transactions on Information Theory 51(12):4252~4262
Hai Q. Dinh / 2009 / Constacyclic Codes of Length $2^s$ Over Galois Extension Rings of ${\BBF}_{2}+u{\BBF}_2$ / IEEE Transactions on Information Theory 55(4):1730~1740
G. Castagnoli / 1991 / On repeated-root cyclic codes / IEEE Transactions on Information Theory 37(2):337~342
B. Chen / 2016 / Constacyclic codes of length 2ps over Fpm + uFpm / Finite Fields Appl. 37:108~130
H.Q. Dinh / 2005 / Negacyclic Codes of Length<tex>$2^s$</tex>Over Galois Rings / IEEE Transactions on Information Theory 51(12):4252~4262
Hai Q. Dinh / 2009 / Constacyclic Codes of Length $2^s$ Over Galois Extension Rings of ${\BBF}_{2}+u{\BBF}_2$ / IEEE Transactions on Information Theory 55(4):1730~1740
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