Binary codes with covering radius one: Some new lower bounds
نویسندگان
چکیده
منابع مشابه
Lower Bounds for q-ary Codes with Large Covering Radius
Let Kq(n,R) denote the minimal cardinality of a q-ary code of length n and covering radius R. Recently the authors gave a new proof of a classical lower bound of Rodemich on Kq(n, n−2) by the use of partition matrices and their transversals. In this paper we show that, in contrast to Rodemich’s original proof, the method generalizes to lower-bound Kq(n, n − k) for any k > 2. The approach is bes...
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In [5], we studied binary codes with covering radius one via their characteristic functions. This gave us an easy way of obtaining congruence properties and of deriving interesting linear inequalities. In this paper we extend this approach to ternary covering codes. We improve on lower bounds for ternary 1-covering codes, the so-called football pool problem, when 3 does not divide n − 1. We als...
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The length function lq(r,R) is the smallest length of a q-ary linear code of covering radius R and codimension r. New upper bounds on lq(r, 2) are obtained for odd r ≥ 3. In particular, using the one-to-one correspondence between linear codes of covering radius 2 and saturating sets in the projective planes over finite fields, we prove that
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00290-7