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Abstrakty
In this paper, to obtain the bounds for some classes of repetition codes with covering radius by using various weight and also the same size and different size of length in repetition codes over a finite ring Z32 .
Czasopismo
Rocznik
Tom
Strony
69--77
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Department of Mathematics, Srimad Andavan Arts and Science College (Auto.), Tiruchirappalli - 620 005, Tamilnadu, India
Bibliografia
- [1] T. Aoki, P. Gaborit, M. Harada, M. Ozeki, P. Solé, On the covering radius of Z4 codes and their lattices, IEEE Trans. Inform. Theory 45, no. 6, pp. 2162-2168(1999).
- [2] C. Bachoc, Applications of coding theory to the construction of modular lattices, Journal of Combinatorial Theory, Series A 78 (1997) 92-119.
- [3] E. Bardellotto, F. Fabris, Binary list decoding beyond covering radius. Journal of Information and Optimization Sciences 35 (5-6) (2014) 561-570.
- [4] C. M. Bhandari, C. Durairajan, On the covering radius of Simplex codes, Journal of Discrete Mathematical Sciences and Cryptography 6 (1) (2003) 59-69.
- [5] C. M. Bhandari, M. K. Gupta, A. K. Lal, On Z4 Simplex codes and their Gray images, Springer Berlin Heidelberg, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes 1719 (1999) 170-180.
- [6] A. Bonnecaze, P. Solé, R. A. Calderbank, Quaternary quadratic residue codes and unimodular lattices, IEEE Trans. Inform. Theory 41 (1995) 366-377.
- [7] A. Bonnecaze, P. Solé , C. Bachoc, B. Mourrain, Type II codes over Z4, IEEE Trans. Inform. Theory 43 (1997) 969-976.
- [8] A. Bonnecaze, P. Udaya, Cyclic codes and self-dual codes over F2 + uF2, IEEE Trans. Inform. Theory 45 (4) (1999) 1250-1254.
- [9] P. Chella Pandian, On the covering radius of codes over Z4 with Chinese Euclidean weight, International Journal on Information Theory 4 (4) (2015) 1-8.
- [10] P. Chella Pandian, On the covering radius of codes over Z6, International Journal on Information Theory 5 (2) (2016) 1-9.
- [11] P. Chella Pandian, On codes over Z23 and its covering radius for Lee weight and homogeneous weight, Journal of Information and Optimization Sciences 39 (8) (2018) 1705-1715.
- [12] P. Chella Pandian, Finding the covering radius of codes over Z32 by assigning homogeneous weight, Journal of Asia Mathematika 4 (3) (2020) 46-50.
- [13] D. G. Cohen, G. M. Karpovsky, F. H. Mattson, R. J. Schatz , Covering radius-survey and recent results, IEEE Trans. Inform. Theory 31 (3) (1985) 328-343.
- [14] C. Cohen, A. Lobstein, A.J.N. Sloane, Further results on the covering radius of codes, IEEE Trans. Inform. Theory 32 (5) (1986) 680-694.
- [15] B. K. Dass, Namita Sharma, Rashmi Verma, The packing radius of a poset block code, Discrete Mathematics, Algorithms and Applications 7 (4) 1550045 (10 pages) (2015).
- [16] C. Durairajan, On Covering Codes and Covering Radius of Some Optimal Codes, Ph.D. Thesis, Department of Mathematics, IIT Kanpur, (1996).
- [17] T. Gulliver, M. Harada, Codes Over F3 + uF3 and Improvements to the Bounds on Ternary Linear Codes, University of Canterbury and Yamagata University, New Zealand and Japan, June 1998.
- [18] K. M. Gupta, G. D. Glynn, T. Aaron Gulliver, On Senary Simplex Codes. In International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Springer, Berlin Heidelberg) (2001) 112-121.
- [19] R. A. Hammons, P. V. Kumar, A. R. Calderbank, P. Sol’e, The Z4-linearity of Kerdock, Preparata, Gothals and related codes, IEEE Trans. Inform. Theory 40 (1994) 301-319.
- [20] B. Yildiz, Z. Ödemis Özger, A generalization of the lee weight to Zpk , TWMS J. App. Eng. Math. 2 (2) (2012) 145-153.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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