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A note on nonlinear Xing codes

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2 Author(s)
Shany, Y. ; Dept. of Electr. Eng.-Syst., Tel-Aviv Univ., Israel ; Be'ery, Y.

Nonlinear Xing codes are considered. It is shown that Xing codes of length p-1 (where p is a prime) are subcodes of cosets of Reed-Solomon codes whose minimum distance equals Xing's lower bound on the minimum distance. This provides a straightforward proof for the lower bound on the minimum distance of the codes. The alphabet size of Xing codes is restricted not to be larger than the characteristic of the relevant finite field Fr. It is shown that codes with the same length and the same lower bounds on the size and minimum distance as Xing codes exist for any alphabet size not exceeding the size r of the relevant finite field, thus extending Xing's results.

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Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 4 )