Number of minimal cyclic codes with given length and dimension

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Publication date: 16 June 2014

Abstract: In this article, we count the quantity of minimal cyclic codes of length

n

and dimension

k

over a finite field

m a t h b b F_{q}

, in the case when the prime factors of

n

satisfy a special condition. This problem is equivalent to count the quantity of irreducible factors of

x^{n} - 1 i n m a t h b b F_{q} [x]

of degree

k

.

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