We obtain structural results about group ring codes over F[G], where F is a finite field of characteristic p > 0 and the Sylow p-subgroup of the Abelian group G is cyclic. As a special case, we characterize cyclic codes over finite fields in the case the length of the code is divisible by the characteristic of the field. By the same approach we study cyclic codes of length m over the ring R = F q [u], u r = 0 with r > 0, gcd(m, q) = 1. Finally, we give a construction of quasi-cyclic codes over finite fields.
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机译：我们获得关于F [G]上的组环码的结构结果，其中F是特征p> 0的有限域，而Abelian组G的Sylow p-子组是循环的。作为一种特殊情况，当代码的长度可被字段的特性整除时，我们将在有限字段上表征循环代码。通过相同的方法，我们研究环上长度为m的循环码R = F q [u]，u r = 0，其中r> 0，gcd（m，q ）=1。最后，我们给出了有限域上的准循环码的构造。
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