On calculation of the interweight distribution of an equitable partition

TL;DR

This paper develops recursive and explicit formulas for the interweight distribution of equitable partitions in hypercubes, utilizing a three-variable generalization of Krawtchouk polynomials, advancing combinatorial and coding theory analysis.

Contribution

It introduces new formulas involving a three-variable Krawtchouk polynomial generalization for calculating interweight distributions in hypercube partitions.

Findings

Derived recursive formulas for interweight distribution.

Provided explicit formulas involving generalized Krawtchouk polynomials.

Enhanced understanding of equitable partitions in hypercubes.

Abstract

We derive recursive and direct formulas for the interweight distribution of an equitable partition of a hypercube. The formulas involve a three-variable generalization of the Krawtchouk polynomials. Keywords: equitable partition; regular partition; partition design; strong distance invariance; interweight distribution; distance distribution; Krawtchouk polynomial