Cyclic codes over R = F_p + uF_p ++ u^k−1F_p with length p^sn

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• 作者：Mu Han ; Youpei Ye ; Shixin Zhu ; Chungen Xu ; Bennian Dou
• 关键词：Cyclic codes ; Galois ring ; Ideal ; Discrete Fourier transform ; Generator polynomial representation
• 刊名：Information Sciences
• 出版年：2011
• 出版时间：15 February 2011
• 年：2011
• 卷：181
• 期：4
• 页码：926-934
• 全文大小：230 K

文摘

In this paper, all cyclic codes with length p^sn, (n prime to p) over the ring R = F_p + uF_p ++ u^k−1F_p are classified. It is first proved that Tor_j(C) is an ideal of , so that the structure of ideals over extension ring S_u^k(m,ω)=GR(u^k,m)[ω]/ω^ps-1 is determined. Then, an isomorphism between R[X]/X^N − 1 and a direct sum _hIS_u^k(m_h,ω) can be obtained using discrete Fourier transform. The generator polynomial representation of the corresponding ideals over F_p + uF_p ++ u^k−1F_p is calculated via the inverse isomorphism. Moreover, torsion codes, MS polynomial and inversion formula are described.