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Some constructions of mutually orthogonal latin squares and superimposed codes

Journal Article


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Abstract


  • Superimposed codes is a special combinatorial structure that has many applications in information theory, data communication and cryptography. On the other hand, mutually orthogonal latin squares is a beautiful combinatorial object that has deep connection with design theory. In this paper, we draw a connection between these two structures. We give explicit construction of mutually orthogonal latin squares and we show a method of generating new larger superimposed codes from an existing one by using mutually orthogonal latin squares. If n denotes the number of codewords in the existing code then the new code contains n2 codewords. Recursively, using this method, we can construct a very large superimposed code from a small simple code. Well-known constructions of superimposed codes are based on algebraic Reed–Solomon codes and our new construction gives a combinatorial alternative approach.

Publication Date


  • 2012

Citation


  • Seberry, J. & Tonien, D. (2012). Some constructions of mutually orthogonal latin squares and superimposed codes. Discrete Mathematics, Algorithms and Applications, 4 (3), 1250022-1-1250022-8.

Scopus Eid


  • 2-s2.0-85073110774

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1583&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/577

Start Page


  • 1250022-1

End Page


  • 1250022-8

Volume


  • 4

Issue


  • 3

Place Of Publication


  • Singapore

Abstract


  • Superimposed codes is a special combinatorial structure that has many applications in information theory, data communication and cryptography. On the other hand, mutually orthogonal latin squares is a beautiful combinatorial object that has deep connection with design theory. In this paper, we draw a connection between these two structures. We give explicit construction of mutually orthogonal latin squares and we show a method of generating new larger superimposed codes from an existing one by using mutually orthogonal latin squares. If n denotes the number of codewords in the existing code then the new code contains n2 codewords. Recursively, using this method, we can construct a very large superimposed code from a small simple code. Well-known constructions of superimposed codes are based on algebraic Reed–Solomon codes and our new construction gives a combinatorial alternative approach.

Publication Date


  • 2012

Citation


  • Seberry, J. & Tonien, D. (2012). Some constructions of mutually orthogonal latin squares and superimposed codes. Discrete Mathematics, Algorithms and Applications, 4 (3), 1250022-1-1250022-8.

Scopus Eid


  • 2-s2.0-85073110774

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1583&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/577

Start Page


  • 1250022-1

End Page


  • 1250022-8

Volume


  • 4

Issue


  • 3

Place Of Publication


  • Singapore