Skew cyclic codes over F_p+uF_p

12/21/2017

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by   Reza Dastbasteh, et al.

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In this paper, we study skew cyclic codes with arbitrary length over the ring R=F_p+uF_p where p is an odd prime and We characterize all skew cyclic codes of length n as left ]-submodules of R_n=R[x;θ ]/〈 x^n-1〉 . We find all generator polynomials for these codes and describe their minimal spanning sets. Moreover, an encoding and decoding algorithm is presented for skew cyclic codes over the ring R. Finally, based on the theory we developed in this paper, we provide examples of codes with good parameters over F_p with different odd prime p. In fact, example 25 in our paper is a new ternary code in the class of quasi-twisted codes. The other examples we provided are examples of optimal codes.