Ring geometries, two-weight codes, and strongly regular graphs
نویسندگان
چکیده
منابع مشابه
Ring geometries, two-weight codes, and strongly regular graphs
It is known that a linear two-weight code C over a finite field Fq corresponds both to a multiset in a projective space over Fq that meets every hyperplane in either a or b points for some integers a < b , and to a strongly regular graph whose vertices may be identified with the codewords of C . Here we extend this classical result to the case of a ring-linear code with exactly two nonzero homo...
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(otherwise we divide the vector by an appropriate scalar), so w.l.o.g. we have uj = 1 for a certain j ∈ {1, . . . , v}. The absolute value |(A~u)j| of the j-th component of A~u is at most ∑ i∼j |ui|; since the absolute values of all components of ~u are less than or equal to 1, we have ∑ i∼j |ui| ≤ k. On the other hand |(A~u)j| must be equal to |ρuj| = |ρ|, from which we obtain |ρ| ≤ k. If ρ = ...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2008
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-007-9136-8