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The 7th Mediterranean International Conference of Pure & Applied Mathematics and Related Areas (MICOPAM 2024), Antalya, Turkey, 26 - 29 October 2024, pp.316-318, (Full Text)
An (n, k, r) locally recoverable code is a code of length n and dimension k if a symbol in any coordinate of a codeword can be recovered by accessing at most r other coordinates. A code with (r, δ)-locality is a locally recoverable code that allows recovering δ − 1 erasures simultaneously by accessing at most r other coordinates. Cyclic codes are very efficient codes due to their encoding and decoding procedures. In this study, we will show that a cyclic code has a constacyclic punctured subcode with its generator polynomial and get parameters of it with (r, δ)-locality. Then we will obtain the structure of cyclotomic cosets with respect to some conditions for n = (q+1)/2 . We will construct cyclic codes with (r, δ)-locality by using their negacyclic punctured subcodes of length (q+1)/2 which are generated by their generator polynomials.