环F2[u]/(u4)上的一类常循环码及其Gray象
doi: 10.3724/SP.J.1146.2012.00869
A Class of Constacyclic Codes OverF2[u]/(u4)and Its Gray Image
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摘要: 该文定义了环R=F2+uF2+u2F2+u3F2到F42的一个新的Gray映射，其中u4=0。证明了R上长为n的(1+u+u2+u3)-循环码的Gray象是F2上长为4n的距离不变的线性循环码。进一步确定了R上奇长度的该常循环码的Gray象的生成多项式，并得到了一些最优的二元线性循环码。Abstract: A new Gray map is defined fromR=F2+uF2+u2F2+u3F2 toF42 with u4=0. It is proved that the Gray image of a linear (1+u+u2+u3)-cyclic code of lengthn over R is a distance-invariant linear cyclic code of length4n over F2. Further more, the generator polynomials of the Gray image of this constacyclic code for odd length over Ris determined, some optimal binary linear cyclic codes are also obtained.
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Key words:
- Cyclic codes /
- Constacyclic codes /
- Generator polynomial
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