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- W4386095208 abstract "In this paper, we investigate the number of irreducible polynomials of (smalllangle)(mathit{x})(mathit{n}) -1(smallrangle) over GF(23). First, We factorize (smalllangle)(mathit{x})(mathit{n}) -1(smallrangle) into irreducible polynomials over GF(23) using the cyclotomic cosets of 23 modulo (mathit{n}). The number of irreducible polynomial factors of (smalllangle)(mathit{x})(mathit{n}) -1(smallrangle) over GF(23) is equal to the number of cyclotomic cosets of 23 modulo n and each monic divisor of (smalllangle)(mathit{x})(mathit{n}) -1(smallrangle) is a generator polynomial of cyclic codes in GF(23). Succeedingly, we confirm that the number of cyclic codes of length (mathit{n}) over (mathit{a}) finite field GF(23) is equivalent to the number of polynomials that divide (smalllangle)(mathit{x})(mathit{n}) -1(smallrangle). In conclusion, we enumerate the number of cyclic codes of length n for l (le) (mathit{n}) < 24 and as (mathit{n}) = 23(mathit{k}) for l (leqslant) (mathit{k}) < 24" @default.
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- W4386095208 date "2023-08-22" @default.
- W4386095208 modified "2023-10-05" @default.
- W4386095208 title "Enumeration of Cyclic Codes Over GF(23)" @default.
- W4386095208 doi "https://doi.org/10.9734/jamcs/2023/v38i91815" @default.
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