대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제55권1호
  • /
  • Pages.115-137
  • /
  • 2018
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CYCLIC CODES OVER THE RING 𝔽p[u, v, w]/〈u2, v2, w2, uv - vu, vw - wv, uw - wu〉

  • Kewat, Pramod Kumar (Department of Applied Mathematics Indian Institute of Technology (ISM)) ;
  • Kushwaha, Sarika (Department of Applied Mathematics Indian Institute of Technology (ISM))
  • 투고 : 2016.10.26
  • 심사 : 2017.03.07
  • 발행 : 2018.01.31
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초록

Let $R_{u{^2},v^2,w^2,p}$ be a finite non chain ring ${\mathbb{F}}_p[u,v,w]{\langle}u^2,\;v^2,\;w^2,\;uv-vu,\;vw-wv,\;uw-wu{\rangle}$, where p is a prime number. This ring is a part of family of Frobenius rings. In this paper, we explore the structures of cyclic codes over the ring $R_{u{^2},v^2,w^2,p}$ of arbitrary length. We obtain a unique set of generators for these codes and also characterize free cyclic codes. We show that Gray images of cyclic codes are 8-quasicyclic binary linear codes of length 8n over ${\mathbb{F}}_p$. We also determine the rank and the Hamming distance for these codes. At last, we have given some examples.

키워드

Table 1. Non zero cyclic codes of length 4 over Ru2,v2,w2,2.

E1BMAX_2018_v55n1_115_t0001.png 이미지

Table 2. Non zero cyclic codes of length 3 over Ru2,v2,w2,3.

E1BMAX_2018_v55n1_115_t0002.png 이미지

Table 3. Non zero cyclic codes of length 5 over Ru2,v2,w2,5.

E1BMAX_2018_v55n1_115_t0003.png 이미지

참고문헌

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