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- W2992381275 abstract "Let $$mathbb {F}_{2^m}$$ be a finite field of $$2^m$$ elements and denote $$R=mathbb {F}_{2^m}[u]/langle u^krangle $$ $$=mathbb {F}_{2^m}+umathbb {F}_{2^m}+cdots +u^{k-1}mathbb {F}_{2^m}$$ ( $$u^k=0$$ ), where k is an integer satisfying $$kge 2$$ . For any odd positive integer n, an explicit representation for every self-dual cyclic code over R of length 2n and a mass formula to count the number of these codes are given. In particular, a generator matrix is provided for the self-dual 2-quasi-cyclic code of length 4n over $$mathbb {F}_{2^m}$$ derived by an arbitrary self-dual cyclic code of length 2n over $$mathbb {F}_{2^m}+umathbb {F}_{2^m}$$ and a Gray map from $$mathbb {F}_{2^m}+umathbb {F}_{2^m}$$ onto $$mathbb {F}_{2^m}^2$$ . Finally, the hull of each cyclic code with length 2n over $$mathbb {F}_{2^m}+umathbb {F}_{2^m}$$ is determined and all distinct self-orthogonal cyclic codes of length 2n over $$mathbb {F}_{2^m}+umathbb {F}_{2^m}$$ are listed." @default.
- W2992381275 created "2019-12-13" @default.
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- W2992381275 date "2019-12-05" @default.
- W2992381275 modified "2023-09-24" @default.
- W2992381275 title "On self-duality and hulls of cyclic codes over $$frac{mathbb {F}_{2^m}[u]}{langle u^krangle }$$ with oddly even length" @default.
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- W2992381275 doi "https://doi.org/10.1007/s00200-019-00408-9" @default.
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