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ARPN Journal of Science and Technology >> Volume 7, Issue 1, January 2017

ARPN Journal of Science and Technology


Covering Radius of RM Binary Codes

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Author O.P.Vinocha, J.S.Bhullar, B.S.Brar
ISSN 2225-7217
On Pages 223-233
Volume No. 4
Issue No. 3
Issue Date April 01, 2014
Publishing Date April 01, 2014
Keywords Reed-Muller code, binary self-complementary code, cosset, weight, strength, covering radius, relation, generalization



Abstract

The strength and the covering radius of a binary self-complementary code are studied under different conditions. Some results for covering radius are found with different range of values of weight of code. We have generalized the results concerning relation between strength and covering radius of code. Then we have proved the result for binary code C of length n having strength s, which represents the relation among n, s, weight of codeword, and number of codewords in code C. Further we have analyzed the particular results by using this relation for code C having strength more than 2, i.e. for strength s = 3, 4, 5, and obtained the range of values of covering radius. Lastly, we have analyzed the values of covering radius and found that in case of even suffix, the values are clear-cut fixed; but in case of odd suffix, only values of r1 , r3 are fixed but afterwards the values become more and more scattered and problem of fixing unique value become more and more difficult.


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