A construction of product blocks with a fixed block size

TL;DR

This paper explores the design of product blocks with fixed size to construct permutation arrays with large size and guaranteed minimum Hamming distance, advancing combinatorial design methods.

Contribution

It introduces a new approach for constructing permutation arrays using fixed-size product blocks, expanding the toolkit for combinatorial design.

Findings

New methods for designing $(q,k)$-product blocks

Improved bounds on permutation array sizes

Enhanced understanding of block-based permutation array construction

Abstract

Let $M(n,d)$ be the maximum size of a permutation array on $n$ symbols with pairwise Hamming distance at least $d$. Some permutation arrays can be constructed using blocks of certain type [2] called product blocks in this paper. We study the problem of designing $(q,k)$-product blocks with a fixed block size $k$.