Applications of Fixed Minimum Distance Codes with Generators in Standard Form


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Authors

  • Mustafa ÖZKAN Trakya University

Keywords:

Mathematical Modeling of Communication, Coding Theory, Linear Codes, Generator Matrices

Abstract

In this study, basic information about algebra and coding theory is mentioned. Afterwards,
generator matrices that produce a linear code are written in standard form, a classification of code types
corresponding to codes with parameters (n + 1,4n,2) of the codes produced by these matrices and
examples are presented. It has been generalized using the same ring as in my work in References [6].

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Author Biography

Mustafa ÖZKAN, Trakya University

Mathematics and life Science Department / Faculty of Education, Turkiye

References

Bose , R.C. and Ray- Chaudhuri , D.K. , On a Class of Error Correcting Binary Group Codes . Information Control, 3: 68-79, 1960.

Delsarte , P. , Bilinear Forms Over A Finite Field , With Applications To Coding Theory . Journal of Combinatorial Theory A, 25: 226–241, 1978.

Lemmermeyer F. , Error-correcting Codes , 2005.

Lin , S. , Xing , C., Coding Theory -A first course CambridgeUniversity , 2004 .

Loidreau , P. , A Welch-Berlekamp Like algorithm for decoding Gabiduline codes . WWC, 36-45, 2005.

Ozkan, M. and Ozturk, B. , Certain Rings and Group Codes . Journal of New Results in Engineering and Natural Science , (8), 25-30,2018.

Pless , V. , Introduction to the Theory of Error-Correcting Codes , 1989.

Roman S. , Coding and Information Theory . Graduate Text in Mathematics , Springer Verlag , 1992.

Shannon , C.E. , A Mathematical Theory of Communication . Bell Sys . tech . J. , pp.379-423 Part 1; pp . 623-656 Part 2, 1948.

Huffman W.C., Pless V. , Fundamentals of Error Correcting Codes , Cambridge, 2003.

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Published

2024-12-30

How to Cite

ÖZKAN, M. (2024). Applications of Fixed Minimum Distance Codes with Generators in Standard Form. International Journal of Advanced Natural Sciences and Engineering Researches, 8(11), 708–715. Retrieved from https://as-proceeding.com/index.php/ijanser/article/view/2342

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