An explicit formula for a weight enumerator of linear-congruence codes
Taro Sakurai (Chiba University)
TL;DR
This paper derives an explicit formula for the weight enumerator of linear-congruence codes, extending previous binary results to non-binary cases, simplifying proofs, and solving an open problem.
Contribution
It provides a generalized explicit formula for non-binary linear-congruence codes, simplifying prior proofs and completing a previously posed open problem.
Findings
Explicit formula for non-binary weight enumerator
Simplified proof of the formula
Complete solution to the open problem
Abstract
An explicit formula for a weight enumerator of linear-congruence codes is provided. This extends the work of Bibak and Milenkovic [IEEE ISIT (2018) 431-435] addressing the binary case to the non-binary case. Furthermore, the extension simplifies their proof and provides a complete solution to a problem posed by them.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · DNA and Biological Computing