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Enumeration of complementary-dual cyclic \(\mathbb{F}_q\)-linear \(\mathbb{F}_{q^t}\)-codes. (English) Zbl 1415.94488

Summary: Let \(\mathbb{F}_q\) denote the finite field of order \(q,n\) be a positive integer coprime to \(q\), and let \(t \geq 2\) be an integer. In this paper, we provide enumeration formulae for all complementary-dual cyclic \(\mathbb{F}_q\)-linear \(\mathbb{F}_{q^t}\)-codes of length \(n\) by placing \(\ast\), ordinary and Hermitian trace inner products on \(\mathbb{F}_{q^t}^n\).

MSC:

94B15 Cyclic codes
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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References:

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