New lower bounds for covering codes
نویسندگان
چکیده
منابع مشابه
Some new lower bounds for ternary covering codes
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...
متن کاملNew upper bounds for binary covering codes
Improved upper bounds are presented for K(n, r), the minimum cardinality of a binary code of length n and coveting radius r. The new bounds are obtained by both new and old constructions; in many of these, computer search using simulated annealing and tabu search plays a central role. Some new linear coveting codes are also presented. An updated table of upper bounds on K(n,r), n~<64, r~<12, is...
متن کاملLower 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...
متن کاملNew Lower Bounds for Matching Vector Codes
A Matching Vector (MV) family modulo m is a pair of ordered lists U = (u1, . . . , ut) and V = (v1, . . . , vt) where ui, vj ∈ Znm with the following inner product pattern: for any i, 〈ui, vi〉 = 0, and for any i 6= j, 〈ui, vj〉 6 = 0. A MV family is called q-restricted if inner products 〈ui, vj〉 take at most q different values. Our interest in MV families stems from their recent application in t...
متن کاملNew lower bounds for constant weight codes
with M (which is expected). However, as M increases beyond Ahstrart -Some new lower bounds are given for A(n,4, IV), the maximum number of codewords in a binary code of length n, min imum distance 4, and constant weight IV. In a number of cases the results significantly 1.0 improve on the best bounds previously known. h=O 1 .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00011-x