New Constructions of a Family of 2-Generator Quasi-Cyclic Two-Weight Codes and Related Codes
Eric Zhi Chen
TL;DR
This paper introduces a novel construction method for 2-generator quasi-cyclic two-weight codes based on cyclic simplex codes, resulting in new optimal and good codes over binary and ternary fields with specific parameters.
Contribution
It presents a new construction approach for quasi-cyclic two-weight codes, producing several optimal binary and good ternary codes, and also constructs binary quasi-cyclic self-complementary codes.
Findings
Constructed new optimal binary quasi-cyclic codes with parameters [195, 8, 96], [210, 8, 104], [240, 8, 120]
Developed good ternary quasi-cyclic codes with parameters [195, 6, 126], [208, 6, 135], [221, 6, 144]
Built binary quasi-cyclic self-complementary codes
Abstract
Based on cyclic simplex codes, a new construction of a family of 2-generator quasi-cyclic two-weight codes is given. New optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, good QC ternary [195, 6, 126], [208, 6, 135], [221, 6, 144] codes are thus obtained. Furthermre, binary quasi-cyclic self-complementary codes are also constructed.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cancer Mechanisms and Therapy