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 n × m matrices with entries in the set [p] = {0, 1, … p − 1}. 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  [p] to be canonical. For this purpose, the matrices are uniquely represented by ordered n-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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  7. Yordzhev, K. (2017) On the cardinality of a factor set of binary matrices. Linear Algebra and Its Applications, 534, 122–134.

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Cite this paper

APA

Yordzhev, K. (2018). Canonical matrices with entries integers modulo p. Notes on Number Theory and Discrete Mathematics, 24(4), 133-143, doi: 10.7546/nntdm.2018.24.4.133-143.

Chicago

Yordzhev, Krasimir. “Canonical Matrices with Entries Integers Modulo p.” Notes on Number Theory and Discrete Mathematics 24, no. 4 (2018): 133-143, doi: 10.7546/nntdm.2018.24.4.133-143.

MLA

Yordzhev, Krasimir. “Canonical Matrices with Entries Integers Modulo p.” Notes on Number Theory and Discrete Mathematics 24.4 (2018): 133-143. Print, doi: 10.7546/nntdm.2018.24.4.133-143.

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