Jacobi polynomials for the first-order generalized Reed--Muller codes
Ryosuke Yamaguchi
TL;DR
This paper derives Jacobi polynomials for first-order generalized Reed--Muller codes and demonstrates the nonexistence of certain combinatorial 3-designs within these codes.
Contribution
It introduces explicit Jacobi polynomials for these codes and establishes a new nonexistence result for specific combinatorial designs.
Findings
Jacobi polynomials for first-order generalized Reed--Muller codes derived
Nonexistence of combinatorial 3-designs in these codes proven
Abstract
In this paper, we give the Jacobi polynomials for first-order generalized Reed--Muller codes. We show as a corollary the nonexistence of combinatorial -designs in these codes.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications