Homogeneity Theorems on Perfect Codes in Hamming Schemes and Generalized Hamming Schemes
نویسندگان
چکیده
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...
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To each association scheme G and to each field R, there is associated naturally an associative algebra, the so-called adjacency algebra RG of G over R. It is well-known that RG is semisimple if R has characteristic 0. However, little is known if R has positive characteristic. In the present paper, we focus on this case. We describe the algebra RG if G is a Hamming scheme (and R a field of posit...
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This paper precisely characterizes secret sharing schemes based on arbitrary linear codes by using the relative dimension/length profile (RDLP) and the relative generalized Hamming weight (RGHW). We first describe the equivocation Δm of the secret vector s = [s1, . . . ,sl ] given m shares in terms of the RDLP of linear codes. We also characterize two thresholds t1 and t2 in the secret sharing ...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1985
ISSN: 0387-3870
DOI: 10.3836/tjm/1270151223