x = (x0,x1,··· ,xnâ1) â Zn. 4 is an arbitrary vector, and suppose Ï(xj)=(xj,0,xj,1) for all j = 0,1,··· ,n â 1, then. Ï(x0,x1,··· ,xnâ1)=(x0,0,x1,0,··· ,xnâ1,0,x0,1,x1,1,··· ,xnâ1,1). (2.3). In this paper, we shall consid
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Sep 3, 2012 - [x,y] = x1y1 + à¸à¸à¸ + xnyn. For any code C over R, we define the orthogonal to be. C⥠= {x â Rn â£. â£[x,c]=0, âc â C}. Throughout the paper we assume that the rings are all Frobenius, see [8] for a definition of this cla
C⥠= {(x|y)|(x,y) â Zα. 2 à Zβ. 4 ,ã(x|y),(v|w)ã = 0 for all (v|w) â C}. The code C is called self-orthogonal if CâC⥠and self-dual if C = Câ¥. It is immediate that the dual code C⥠of C is an additive code. We denote the minimum
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Oct 23, 2015 - reduction µ from Râ[x] to F2[x] where µ(f) = µ(âaixi) = âµ(ai)xi. A monic polynomial f over Râ[x] is said to be a basic irreducible poly- nomial if ...
Apr 19, 2012 - Additionally, ai does not contain any of the u1,u2,... .... (a1,a2), where the ai are units, must be generated by that vector and hence be a one-.
4 Oct 2011 - If the code is a submodule then we say that the code is a linear code (over Z2k ). If C is a code over Z2k , then. ãCã is the code over Z2k spanned by the vectors in C. If v, w â Zn. 2k , v = (v1,...,vn), w = (w1,...,wn), we define
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