대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제56권6호
  • /
  • Pages.1385-1422
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  • 2019
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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NEGACYCLIC CODES OF LENGTH 8ps OVER Fpm + uFpm

  • Klin-eam, Chakkrid (Department of Mathematics Faculty of Science Naresuan University) ;
  • Phuto, Jirayu (Department of Mathematics Faculty of Science Naresuan University)
  • 투고 : 2018.08.01
  • 심사 : 2019.04.25
  • 발행 : 2019.11.30
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초록

Let p be an odd prime. The algebraic structure of all negacyclic codes of length $8_{p^s}$ 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 $8_{p^s}$ over ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ into 5 cases, i.e., $p^m{\equiv}1$ (mod 16), $p^m{\equiv}3$, 11 (mod 16), $p^m{\equiv}5$, 13 (mod 16), $p^m{\equiv}7$, 15 (mod 16) and $p^m{\equiv}9$ (mod 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

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