MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES

Seda Akbıyık

MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES

Abstract

Codes over various metrics such as Rosenbloom-Tsfasman (RT), Lee, etc. have been considered in the literature. Recently, codes over poset metrics have been studied. Poset metric is a great generalization of many metrics especially the well-known ones such as the RT and the Hamming metrics. Poset metric can be realized on the channels with localized error occurrences. It has been shown that MacWilliams identities are not admissible for codes over poset metrics in general [15]. Lately, to overcome this problem some further studies on MacWilliams identities over poset metrics has been presented. In this paper, we introduce new poset level weight enumerators of linear codes over Frobenius commutative rings. We derive MacWilliams-type identities for each of the given enumerators which generalize in great deal the previous results discussed in the literature. Most of the weight enumerators in the literature such as Hamming, Rosenbloom-Tsfasman and complete m-spotty weight enumerators follow as corollaries to these identities especially.

Keywords

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Seda Akbıyık This is me
0000-0003-1797-674X
Türkiye

Publication Date

June 1, 2018

Submission Date

December 26, 2017

Acceptance Date

April 9, 2018

Published in Issue

Year 2018 Volume: 36 Number: 2

IZ

https://izlik.org/JA52YA97HW

Cite

RIS / Bibtex

APA

Akbıyık, S. (2018). MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES. Sigma Journal of Engineering and Natural Sciences, 36(2), 405-418. https://izlik.org/JA52YA97HW

AMA

1.Akbıyık S. MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES. SIGMA. 2018;36(2):405-418. https://izlik.org/JA52YA97HW

Chicago

Akbıyık, Seda. 2018. “MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES”. Sigma Journal of Engineering and Natural Sciences 36 (2): 405-18. https://izlik.org/JA52YA97HW.

EndNote

Akbıyık S (June 1, 2018) MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES. Sigma Journal of Engineering and Natural Sciences 36 2 405–418.

IEEE

[1]S. Akbıyık, “MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES”, SIGMA, vol. 36, no. 2, pp. 405–418, June 2018, [Online]. Available: https://izlik.org/JA52YA97HW

ISNAD

Akbıyık, Seda. “MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES”. Sigma Journal of Engineering and Natural Sciences 36/2 (June 1, 2018): 405-418. https://izlik.org/JA52YA97HW.

JAMA

1.Akbıyık S. MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES. SIGMA. 2018;36:405–418.

MLA

Akbıyık, Seda. “MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES”. Sigma Journal of Engineering and Natural Sciences, vol. 36, no. 2, June 2018, pp. 405-18, https://izlik.org/JA52YA97HW.

Vancouver

1.Seda Akbıyık. MACWILLIAMS IDENTITIES FOR POSET LEVEL WEIGHT ENUMERATORS OF LINEAR CODES. SIGMA [Internet]. 2018 Jun. 1;36(2):405-18. Available from: https://izlik.org/JA52YA97HW