Binary and Ternary Quasi-perfect Codes with Small Dimensions
Tsonka Baicheva, Iliya Bouyukliev, Stefan Dodunekov, and Veerle Fack
TL;DR
This paper systematically investigates small-dimensional quasi-perfect binary and ternary linear codes, providing classifications, infinite families, and sporadic examples to advance understanding of their parameters and structures.
Contribution
It offers a complete classification of small-dimensional binary and ternary QP codes, including infinite families and sporadic examples, expanding existing knowledge.
Findings
List of infinite families of QP codes for binary, ternary, and quaternary cases
Complete classification of binary QP codes up to dimension 14
Complete classification of ternary QP codes up to dimension 13
Abstract
The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of infinite families of QP codes which includes all binary, ternary and quaternary codes known to is. We continue further with a list of sporadic examples of binary and ternary QP codes. Later we present the results of our investigation where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions up to 13 are classified.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research