By W.B. Vasantha Kandasamy, Florentin Smarandache, N. Suresh Babu, R.S. Selvaraj
ISBN-10: 9185917125
ISBN-13: 9789185917129
The hot type of rank distance m-codes might be necessary within the m-public key m-cryptosystems (m>1) and m-redundant array of cheap disks. AMRD-m-codes can be utilized in information multi (m)-storage structures. those m-codes offer a cost-effective, time-saving substitute.
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Extra resources for Rank Distance Bicodes and Their Generalization
Example text
46: Let f n1 f n2 { f u11 u1 V n1 } { f u22 u2 V n2 } . Let \ \ 1 \ 2 :V n V n o f n f n defined by \ ( u1 ) \ ( u2 ) f u1 f u2 . Clearly \1 is a bijection 1 2 1 1 2 2 and \2 is a bijection. Let C1[n1, k1, d1] C2[n2, k2, d2] be an RD bicode which is a subbispace of V n1 V n2 of bidimension k1 k2 and minimum rank bidistance d1 d2. Then \ 1 ( C1 ) \ 2 ( C2 ) f n1 f n2 is a fuzzy RD bicode. If c = c1 c2 C1 C2 then f c1 f c2 is a fuzzy bicodeword of \ 1 ( C1 ) \ 2 ( C2 ) .
Then from each biblock almost one bivector can be chosen such that the selected bivectors are atleast rank 2 apart from each other. Such a biset we call as a (n1, 1, 2) (n2, 1, 2) biset. Also it is always possible to construct such a biset. Thus A(n1, 1, 2) A(n2, 1, 2) 2n1 1 2n 2 1 . e. A(ni, ni, ni) = 2N – 1; i = 1, 2); over any GF(2N). Proof: Denote by Vn1 Vn 2 ; the biset of all bivectors of birank n1 n2 in the bispace V n1 V n 2 . We know the bicardinality of Vn1 Vn 2 is (2N – 1) (2N – 2) … (2 N 2n1 1 ) (2N – 1) (2N – 2) … (2 N 2n 2 1 ) , by the definition of a (n1, n1, n1) (n2, n2, n2) biset the bidistance between any two bivectors should be n1 n2.
Thus with each D = D1 E2 GF(2N) GF(2N), we can associate a T1 T2 circulant bimatrix whose ith bicolumn represents D i C1 E i C2 ; i = 0, 1, 2, …, N – 1. f = f1 f2 is nothing but a bimapping of GF(2N) GF(2N) on to the pseudo false bialgebra of all N u N circulant bimatrices over GF(2). Denote the bispace f(GF(2N)) = f1(GF(2N)) f2(GF(2N)) by VN VN. We define binorm of a biword v = v1 v2 VN VN as follows. 15: The binorm of a biword v = v1 v2 VN VN is defined as the birank of v = v1 v2 over GF(2N) (by considering it as a circulant bimatrix over GF(2)).