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Group Partitions and Mixed Perfect Codes

Published online by Cambridge University Press:  20 November 2018

Bernt Lindström
Bernt Lindström*
Affiliation:
Department of Mathematics, University of Stockholm, Box 6701, S-113 85 Stockholm, Sweden Emaljvägen 14VS-175 73 Järfälla, Sweden
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Abstract

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Let G be a finite abelian group of the order pr and type (p, …, p), where p is a prime. A necessary and sufficient condition is determined for the existence of subgroups G1, G2, ⋯, Gn, one of the order pa and the rest of the order pb, such that G = G1 ∪ G2 ∪ ⋯ ∪ Gn and Gi, ∩ Gj,= {θ} when i ≠ j.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 57 - 60
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Herzog, M. and Schönheim, J., Linear and nonlinear single-error-correcting perfect mixed codes, Information and Control 18 (1971), 364-368.Google Scholar
2. Herzog, M. and Schönheim, J., Group partition, factorization and the vector covering problem, Canad. Math. Bull. 15 (2) (1972), 207-214.Google Scholar
3. Lenstra, H. W. Jr., Two theorems on perfect codes, Discrete mathematics 3 (1972), 125-132.Google Scholar