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- W4367000466 abstract "The Euclidean hull of a linear code $C$ is defined as $Ccap C^{perp}$, where $C^perp$ denotes the dual of $C$ under the Euclidean inner product. A linear code with zero hull dimension is called a linear complementary dual (LCD) code. A pair $(C, D)$ of linear codes of length $n$ over $mathbb{F}_q$ is called a linear complementary pair (LCP) of codes if $Coplus D=mathbb{F}_q^n$. In this paper, we give a characterization of LCD and LCP of cyclic codes of length $q^m-1$, $m geq 1$, over the finite field $mathbb{F}_q$ in terms of their basic dual zeros and their trace representations. We also formulate the hull dimension of a cyclic code of arbitrary length over $mathbb{F}_q$ with respect to its basic dual zero. Moreover, we provide a general formula for the dimension of the intersection of two cyclic codes of arbitrary length over $mathbb{F}_q$ based on their basic dual zeros." @default.
- W4367000466 created "2023-04-27" @default.
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- W4367000466 date "2023-04-05" @default.
- W4367000466 modified "2023-09-26" @default.
- W4367000466 title "A note on the hull and linear complementary pair of cyclic codes" @default.
- W4367000466 doi "https://doi.org/10.48550/arxiv.2304.12229" @default.
- W4367000466 hasPublicationYear "2023" @default.
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