Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
394303 | Information Sciences | 2011 | 9 Pages |
Abstract
In this paper, all cyclic codes with length psn, (n prime to p) over the ring R = Fp + uFp +⋯+ uk−1Fp are classified. It is first proved that Torj(C ) is an ideal of S¯=Fpm[ω]/〈ωps-1〉, so that the structure of ideals over extension ring Suk(m,ω)=GR(uk,m)[ω]/〈ωps-1〉Suk(m,ω)=GR(uk,m)[ω]/〈ωps-1〉 is determined. Then, an isomorphism between R[X]/〈XN − 1〉 and a direct sum ⊕h∈ISuk(mh,ω)⊕h∈ISuk(mh,ω) can be obtained using discrete Fourier transform. The generator polynomial representation of the corresponding ideals over Fp + uFp +⋯+ uk−1Fp is calculated via the inverse isomorphism. Moreover, torsion codes, MS polynomial and inversion formula are described.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Mu Han, Youpei Ye, Shixin Zhu, Chungen Xu, Bennian Dou,