Cyclic codes over $\mathbb{F}_{2^m}[u]/\langle u^k\rangle$ of oddly even length
نویسندگان
چکیده
Let F2m be a finite field of characteristic 2 and R = F2m [u]/〈u 〉 = F2m + uF2m + . . . + u k−1 F2m (u k = 0) where k ∈ Z satisfies k ≥ 2. For any odd positive integer n, it is known that cyclic codes over R of length 2n are identified with ideals of the ring R[x]/〈x − 1〉. In this paper, an explicit representation for each cyclic code over R of length 2n is provided and a formula to count the number of codewords in each code is given. Then a formula to calculate the number of cyclic codes over R of length 2n is obtained. Moreover, the dual code of each cyclic code and self-dual cyclic codes over R of length 2n are investigated.
منابع مشابه
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ورودعنوان ژورنال:
- CoRR
دوره abs/1511.05413 شماره
صفحات -
تاریخ انتشار 2015