有限主理想环上接近MDR码

Near-MDR codes over finite principal ideal rings

将有限域上接近MDS码的概念推广到有限主理想环上的接近MDR码。利用有限主理想环上线性码为有限链环上线性码的中国积,将有限主理想环上线性码为接近MDR码的判定转化成有限链环上接近MDR码的判定。进一步,将有限链环上接近MDR码的判定转化为它的剩余类域上接近MDS码的判定,从而描述了有限主理想环上接近MDR码。

The definition of Near-MDS codes over finite fields was generalized to near-MDR codes over finite principal ideal rings. Using the fact that a linear codes over a finite principal ideal ring is the Chinese product of the linear codes over finite chain rings, the criterion of near-MDR codes over finite principal ideal rings are changed into that of near- MDR codes over finite chain rings. Furthermore, the criterion of near-MDR codes over finite chain rings is changed into that of near-MDS codes over residue fields, so we describe near-MDR codes over finite principal ideal rings.