【摘要】 设p,q是两个不同的素数且p≡1(mod4),qp-14≡1(modp),β是Fp中的一个本原元素,α是Fq的某个扩域中的一个本原p次单位根.令R0={β4i(modp)|1≤i≤p-14},g0(x)=∏j∈R0(x-αj).Fq上长度为p,由g0(x)生成的循环码称为四次剩余码,证明了这样码的极小距离d≥4p,并且将本结论推广到任意自然数n(n≥5).更多还原

【Abstract】 Let p and q be two different primes, p≡1(mod 4),qp-14≡1(mod p),β a primitive element of field Fp,α a primitive pth root of unity in an extension field of Fq. Let R0={β4i(mod p)|1≤i≤p-14},g0(x)=∏j∈R0(x-αj). The forth code of length p over Fq with generator g0(x) is called forth residue code. In this paper,it is shown that the minimal distance of the forth residue code is not smaller than 4p.更多还原