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- W1971202639 abstract "Let N and G be finite groups with orders n and g , respectively, and let q be a prime power. Also, let EA( q ) be the elementary abelian group of order q , and let EA( n ) be the group of order n which is the direct product of elementary abelian groups. This paper discusses generalised Hadamard matrices, GH( n ; G ), which are developed modulo a group N . These matrices have been called N -invariant GH-matrices and they are equivalent to G -relative difference sets, RDS( g , n , n , 0, n / g ), modulo the direct sum of N and G . Contained in this paper are simple constructions for GH( q ; EA( q )), q odd, developed modulo EA( q ), and GH( q 2 ; G ), developed modulo EA( q 2 ). Also, an algebraic setting for the study of these designs is developed, and non-existence results are obtained. Indeed, in all but 15 of the 108 cases with n ⩽50, the existence of a GH( n ; EA( q )), developed modulo EA( n ), is either proved or disproved. In addition, a result on the non-existence of generalised weighing matrices developed modulo a group is presented. Finally a connection with error-correcting codes is presented, and it is proved that if n ⩾ g ( g −1) then every element of G must appear in any GH( n ; G ) developed modulo a group." @default.
- W1971202639 created "2016-06-24" @default.
- W1971202639 creator A5055127288 @default.
- W1971202639 date "1992-06-01" @default.
- W1971202639 modified "2023-09-28" @default.
- W1971202639 title "Generalised Hadamard matrices which are developed modulo a group" @default.
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- W1971202639 doi "https://doi.org/10.1016/0012-365x(92)90624-o" @default.
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