有限链环上循环码的深度分布

The Depth Distribution of Linear Cyclic Codes over Finite Chain Ring

研究有限链环R上长为n(n不整除R的剩余域R珚的特征)的循环码的深度分布.根据有限链环R上循环码的生成多项式,从差分运算的线性性质及有限链环上循环码的同构关系出发,给出了有限链环上R上长为n的循环码的深度谱.

The depth distribution of cyclic codes of length n （where n is not divisible by the characteristic of the residue field R ） over a finite chain ring R is studied. By the generator polynomial of cyclic codes over the finite chain R , in light of the linear property of difference operation and the isomorphism of cyclic codes over finite chain ring, the depth spectrum of cyclic codes of length n over a finite chain ring is given.