Abstract
Based on a general construction approach of designs over finite fields by Itoh and some computer results we list five new infinite series of 2-designs over the binary and the ternary field.
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Communicated by T. Etzion.
Appendix: Tables
Appendix: Tables
In this section we list the mentioned designs. Each design is represented by the generators of the prescribed group of automorphisms and corresponding orbit representatives given by generator matrices whose columns form a basis of the corresponding subspaces.
To obtain a compact representation we write a matrix—either an invertible \(n\times n\) matrix representing a general linear group element or an \(n\times k\) generator matrix of a k-dimensional subspace—\(X = [x_{i,j}]\) with entries from the field \({\mathbb {F}}_q\) and indices numbered from 0 as a sequence of integers \([\sum _i x_{i,0}q^i,\sum _i x_{i,1}q^i,\ldots ]\).
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Braun, M. New infinite series of 2-designs over the binary and ternary field. Des. Codes Cryptogr. 81, 145–152 (2016). https://doi.org/10.1007/s10623-015-0133-z
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DOI: https://doi.org/10.1007/s10623-015-0133-z