Partial sums of binomials, intersecting numbers, and the excess bound in Rosenbloom–Tsfasman space
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In this work, the sphere-covering bound on covering codes in Rosenbloom–Tsfasman spaces (RT spaces) is improved by generalizing the excess counting method. The approach focuses on studying the parity of a Rosenbloom–Tsfasman sphere (RT sphere) and the parity of the intersection of two RT spheres. We connect the parity of an RT sphere with partial sums of binomial coefficients and p-adic valuation of binomial coefficients. The intersection number of RT spaces is introduced and we determinate its parity under some conditions. Numerical applications of the method are discussed.
KeywordsRosenbloom–Tsfasman metric Covering code Bounds on code Sum of binomials Congruence
Mathematics Subject Classification94B25 05A10 05A19 06A06
The authors would like to thank the anonymous referees for their suggestions that greatly improved this paper.
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