Canonical matrices with entries integers modulo p

Krasimir Yordzhev
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 4, Pages 133–143
DOI: 10.7546/nntdm.2018.24.4.133-143
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Authors and affiliations

Krasimir Yordzhev
Faculty of Mathematics and Natural Sciences
South-West University “Neofit Rilski”
Blagoevgrad, Bulgaria

Abstract

The work considers an equivalence relation in the set of all matrices with entries in the set . In each element of the factor-set generated by this relation, we define the concept of canonical matrix, namely the minimal element with respect to the lexicographic order. We have found a necessary and sufficient condition for an arbitrary matrix with entries in the set  to be canonical. For this purpose, the matrices are uniquely represented by ordered -tuples of integers.

Keywords

• Permutation matrix
• Weighing matrix
• Hadamard matrix
• Semi-canonical matrix
• Canonical matrix
• Ordered n-tuples of integers

2010 Mathematics Subject Classification

• 05B20
• 15B36

References

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