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Sequence of Numbers of Linear Codes with Increasing Hull Dimensions
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Sequence of Numbers of Linear Codes with Increasing Hull Dimensions
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Sequence of Numbers of Linear Codes with Increasing Hull Dimensions
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Paper
Sequence of Numbers of Linear Codes with Increasing Hull Dimensions
2025
Overview
The hull of a linear code \\(C\\) is the intersection of \\(C\\) with its dual code. We present and analyze the number of linear \\(q\\)-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given dimension \\(k\\) and length \\(n\\ge 2k\\) the number of all \\([n,k]_q\\) linear codes with hull dimension \\(l\\) decreases as \\(l\\) increases. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length \\(n\\) and dimension \\(k\\), comparing the obtained numbers with the number of all linear codes for the given \\(n\\) and \\(k\\).
Publisher
Cornell University Library, arXiv.org
Subject
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