منابع مشابه
Ternary Hamming and binary perfect covering codes
Given 1 1n € Z, the n-cube Q, is the graph with vertex set V : {0, l}' and ed"geset n:VT:orfi, where f' : {(r,w) e V xV: (u _ w)i:1if and only if j: i,(j:0,.'. ,n-l)), for i:0,... ,n-1. The edges of/t aresaidtohave (ortolie along) the directioni,for i 0,.. . ,n-!.Given a graph G, we say that S gVG) is a perfect dom'inating sei (or PDS) of G if every u € V(G) \ S is neighbor of exactly one verte...
متن کاملSome 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 کاملTernary codes through ternary designs
It is known that under certain conditions the incidence matrix of a balanced incomplete block design (v, b, r, k, λ) gives a binary code of length b and size 2(v + 1). Here we investigate the conditions where a balanced ternary design gives a similar ternary code.
متن کاملTernary Constant Weight Codes
Let A3(n, d,w) denote the maximum cardinality of a ternary code with length n, minimum distance d, and constant Hamming weight w. Methods for proving upper and lower bounds on A3(n, d,w) are presented, and a table of exact values and bounds in the range n ≤ 10 is given.
متن کاملClassifying Optimal Ternary Codes of Length 5 and Covering Radius 1
It is well known that optimal ternary codes of length 5 and covering radius 1 have 27 codewords. The structure of such optimal codes has been studied, but a classification of these is still lacking. In this work, a complete classification is carried out by constructing codes coordinate by coordinate in a backtrack search. Linear inequalities and equivalence checking are used to prune the search...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1996
ISSN: 1077-8926
DOI: 10.37236/1281