On the minimum weights of binary linear complementary dual codes
Abstract
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We determine $d(n,4)$ for $n \equiv 2,3,4,5,6,9,10,13 \pmod{15}$, and $d(n,5)$ for $n \equiv 3,4,5,7,11,19,20,22,26 \pmod{31}$. Combined with known results, the values $d(n,k)$ are also determined for $n \le 24$.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.03525
- arXiv:
- arXiv:1807.03525
- Bibcode:
- 2018arXiv180703525A
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Information Theory;
- 94B05
- E-Print:
- 21 pages