1. ON LINEAR COMPLEMENTARY DUAL FOUR CIRCULANT CODES.
- Author
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ZHU, HONGWEI and SHI, MINJIA
- Subjects
- *
LOGICAL prediction , *CIRCULANT matrices , *TOEPLITZ matrices , *ABSTRACT algebra , *WIENER integrals - Abstract
We study linear complementary dual four circulant codes of length $4n$ over $\mathbb{F}_{q}$ when $q$ is an odd prime power. When $q^{\unicode[STIX]{x1D6FF}}+1$ is divisible by $n$ , we obtain an exact count of linear complementary dual four circulant codes of length $4n$ over $\mathbb{F}_{q}$. For certain values of $n$ and $q$ and assuming Artin’s conjecture for primitive roots, we show that the relative distance of these codes satisfies a modified Gilbert–Varshamov bound. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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