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q ‐Analogs of Packing Designs
Author(s) -
Braun Michael,
Reichelt Jan
Publication year - 2014
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21376
Subject(s) - mathematics , linear subspace , automorphism , packing problems , dimension (graph theory) , combinatorics , subspace topology , integer (computer science) , selection (genetic algorithm) , constant (computer programming) , metaheuristic , group (periodic table) , mathematical optimization , discrete mathematics , computer science , pure mathematics , artificial intelligence , mathematical analysis , chemistry , organic chemistry , programming language
AP q ( t , k , n )q ‐packing design is a selection of k ‐dimensional subspaces of F q n such that each t ‐dimensional subspace is contained in at most one element of the collection. A successful approach adopted from the Kramer–Mesner method of prescribing a group of automorphisms was applied by Kohnert and Kurz to construct some constant dimension codes with moderate parameters that arise by q ‐packing designs. In this paper, we recall this approach and give a version of the Kramer–Mesner method breaking the condition that the whole q ‐packing design must admit the prescribed group of automorphisms. Afterwards, we describe the basic idea of an algorithm to tackle the integer linear optimization problems representing the q ‐packing design construction by means of a metaheuristic approach. Finally, we give some improvements on the size ofP 2 ( 2 , 3 , n )q ‐packing designs.