On (1-u2) -cyclic codes over F₂k +uF₂k +u²F₂k
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참고문헌
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초록
It is extended a result of [3] to codes over the commutative ring F₂k + uF₂k + u²F₂k where k ∈ N and u₃ = 0. A new Gray map between codes over F₂k + uF₂k + u²F₂k and F₂k is de ned. It is proved that the Gray image of the linear (1 - u²)-cyclic code over the commutative ring F₂k +uF₂k +u²F₂k of length n is a distance-invariant quasicyclic code of index 2²k-1 and the length 2²kn over F₂k .
Abstract
It is extended a result of [3] to codes over the commutative ring F₂k + uF₂k + u²F₂k where k ∈ N and u₃ = 0. A new Gray map between codes over F₂k + uF₂k + u²F₂k and F₂k is de ned. It is proved that the Gray image of the linear (1 - u²)-cyclic code over the commutative ring F₂k +uF₂k +u²F₂k of length n is a distance-invariant quasicyclic code of index 2²k-1 and the length 2²kn over F₂k .
참고문헌 (4)
- Maria Carmen V.Amarra, "On (1 u) cyclic codes over Fpk + uFpk", Applied Mathematics Letters, ~ (2008)
- M.Greferath, "Gray isometries for nite chain rings and a nonlinear Ternary (36; 312; 15) code", IEEE Trans. Inform. Theory, 45(7), pp.2522~2524 (1999)
- Jian-Fa Qian, "Constacyclic and cyclic codes over F2 + uF2 + u2F2", IEICE Trans. Fundamentals, E89-A(6) (2006)
- Jian-Fa Qian, "constacyclic and cyclic codes over F2 + uF2", Applied Mathematics Letters, 19, pp.820~823 (2006)