Extended LP Bound for LCD codes and New Binary and Ternary LCD Codes

Date

2025-7-3

Author

Emre, Karabakla

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The linear‐programming (LP) methodology proposed by Dougherty et al. originally formulated for binary LCD codes, is generalized herein to arbitrary $q$-ary settings. A unified LP bound is derived that subsumes and strengthens existing binary and ternary limits, yielding strictly tighter theoretical constraints. Within this framework, refined LP‐bound tables for binary LCD codes are presented—augmenting and improving upon previously known entries—and, for the first time, analogous tables for ternary LCD codes are compiled. Several canonical construction results are lifted from the binary and ternary cases to arbitrary $q$, thereby producing novel LCD codes with enhanced parameters. Finally, algebraic analysis of cyclic and quasi‐cyclic structures elucidates new criteria and techniques for the construction of LCD codes, offering insights into their construction.

Subject Keywords

Linear programming bound, linear complementary dual code, Cyclic code, Quasi-cyclic code

URI

https://hdl.handle.net/11511/115176

Collections

Graduate School of Applied Mathematics, Thesis