Recursive methods for some problems in coding and random permutations

TL;DR

This paper explores recursive techniques to analyze problems in coding theory and random permutations, providing new bounds and relations for code parameters and permutation cycle statistics.

Contribution

It introduces recursive methods for estimating code distances, code size convergence, and cycle moments in permutations, advancing theoretical understanding in these areas.

Findings

Estimated minimum distance for locally recoverable codes with partial locality

Proved convergence of minimum code size for weighted lattice codes

Derived recursive formulas for mean and variance of cycle counts in permutations

Abstract

In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next we consider weighted lattice representative codes and use recursive subadditive techniques to obtain convergence of the minimum code size. Finally, we obtain a recursive relation involving cycle moments in random permutations and as an illustration, evaluate recursions for the mean and variance.