On Optimal Anticodes over Permutations with the Infinity Norm

TL;DR

This paper investigates optimal anticodes over permutations under the infinity norm, classifying them for half the parameter range and establishing structural constraints for the rest, linking the problem to matrix permanents.

Contribution

It provides a complete classification of optimal anticodes for half the parameter range and structural insights for the remaining cases, connecting permutation anticodes to matrix permanents.

Findings

Classified all optimal anticodes for half the parameter range.

Established structural constraints for remaining cases.

Linked the problem to the maximum permanent of (0,1)-matrices.

Abstract

Motivated by the set-antiset method for codes over permutations under the infinity norm, we study anticodes under this metric. For half of the parameter range we classify all the optimal anticodes, which is equivalent to finding the maximum permanent of certain $(0,1)$-matrices. For the rest of the cases we show constraints on the structure of optimal anticodes.