共查询到19条相似文献,搜索用时 171 毫秒
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本文研究了环Fp+vFp上互补对偶(1-2v)-常循环码.利用环Fp+vFp上(1-2v)-常循环码的分解式C=vC1-v ⊕(1-v)Cv,得到了环Fp+vFp上互补对偶(1-2v)-常循环码的生成多项式.然后借助从Fp+vFp到Fp2的Gray映射,证明了环Fp+vFp上互补对偶(1-2v)-常循环码的Gray像是Fp的互补对偶循环码. 相似文献
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本文将一类修正的Kdv方程ut+auux + au2ux +μux3+β(1+u2)(1+ux2)(1+ut2)(1+ux32)(ux3+σux 相似文献
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几个非线性演化方程的解析解 总被引:4,自引:0,他引:4
本文我们求出了K—P方程uxt+6(uux)x+uxxxx+3k2uyy=0和Boussinesq方程utt-uxt-6(u2)xx+uxxxx=0的孤立波解族.求出了广义Schr?dinger方程iut+uxx-u相似文献
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本文把这种代数的同构分类问题归结为素域Fp=Z/pZ上2阶一般线性群GL(2,Fp)作用于M4,2(Fp)的2秩阵子集Mp上的轨道条数r(p)的求法问题,并以p=2,3为例具体给出r(2)=42,r(3)=149. 相似文献
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Y. Cengellenmis 《Applied mathematics and computation》2011,218(3):720-722
We define a new map between codes over Fp + uFp + u2Fp and Fp which is different to that defined in [2]. It is proved that the image of the linear cyclic code over the commutative ring Fp + uFp + u2Fp with length n under this map is a distance-invariant quasi-cyclic code of index p2 with length p2n over Fp. Moreover, it is proved that, if (n, p) = 1, then every code with length p2n over Fp which is the image of a linear (1 − u2)-cyclic code with length n over Fp + uFp + u2Fp under this map is permutation equivalent to a quasi-cyclic code of index p2. 相似文献
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In this paper, we study cyclic codes over the rings Z
2 + uZ
2 and Z
2 + uZ
2 + u
2
Z
2 . We find a set of generators for these codes. The rank, the dual, and the Hamming distance of these codes are studied as
well. Examples of cyclic codes of various lengths are also studied.
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In this work, we focus on cyclic codes over the ring
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} , which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et.al. in (Des Codes Crypt 42:273–287,
2007) to characterize the ring
(\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2)/(xn-1){({{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2})/(x^n-1)} and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} under two Gray maps that are defined. We also characterize the binary images of cyclic codes over
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} in general. 相似文献
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We obtain structural results about group ring codes over F[G], where F is a finite field of characteristic p > 0 and the Sylow p-subgroup of the Abelian group G is cyclic. As a special case, we characterize cyclic codes over finite fields in the case the length of the code is divisible
by the characteristic of the field. By the same approach we study cyclic codes of length m over the ring R = F
q
[u], u
r
= 0 with r > 0, gcd(m, q) = 1. Finally, we give a construction of quasi-cyclic codes over finite fields.
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Jianfa Qian Lina Zhang Shixin Zhu 《Journal of Applied Mathematics and Computing》2006,22(1-2):159-167
The transform domain characterization of cyclic codes over finite fields using Discrete Fourier Transform(DFT) over an appropriate extension field is well known. In this paper, we extend this transform domain characterization for cyclic codes overF p +uF p + ··· +u k-1 F p . We give a way to characterize cyclic codes overF p +uF p + ··· +u k-1 F p by Mattson-Solomon polynomials and multiple defining sets. 相似文献