Classification of Hermitian LCD codes extended to new lengths
Classification of binary, ternary and quaternary Hermitian LCD codes
Information Theory
Summary
Hermitian LCD codes are special types of error-correcting codes important in communication and data storage. The authors expanded the known complete lists of these codes to longer lengths for binary, ternary, and quaternary cases. They used a technique that turns finding equivalent codes into a problem of comparing graphs, making the classification process more manageable. This helps people understand all possible codes up to these lengths and how they relate to each other.
What this means in practice
- •For communication engineers: Use the extended classifications to design more efficient error-correcting codes for digital communication systems with guaranteed dual properties.
- •For data storage developers: Access a complete set of Hermitian LCD codes at new lengths to improve data integrity measures in storage devices.
Authors
Keita Ishizuka
Abstract
We extend the complete classifications of linear complementary dual (LCD) codes from length 15 to length 19 in the binary case, from length 10 to length 15 in the ternary case and from length 12 to length 13 in the quaternary Hermitian case. The classification rests on a reduction of the monomial equivalence of LCD codes to graph isomorphism on the coordinates, combined with canonical augmentation.