The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Expanding Generalized Hadamard Matrices over Gm by Using Generalized Hadamard Matrices over G

그룹 G상의 일반화된 하다마드 행렬을 이용한 \ulcorner 상의 일반화된 하다마드 행렬의 확장

  • Published : 2000.10.01
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Abstract

Over an additive abelian group G of order g and for a given positive integer λ, a generalized Hadamard matrix GF(g,λ) is defined as a gλ$\times$gλ matrix [h(i,j)] where 1$\leq$i$\leq$gλ,1$\leq$j$\leq$gλ, such that every element of G appears exactly λ times in the list h(i$_1$,1)-h(i$_2$,1), h(i$_1$,2)-h(i$_2$,2),...,h(i$_1$,gλ)-h(i$_2$, gλ) for any i$\neq$j. In this paper, we propose a new method of expanding a GH(\ulcorner,λ$_1$) = B = \ulcorner over G by replacing each of its m-tuple \ulcorner with \ulcorner GH(g,λ$_2$) where m=gλ$_2$. We may use \ulcornerλ$_1$(not necessarily all distinct) GH(g,λ$_2$)'s for the substitution and the resulting matrix is defined over the group of order g.

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