By W.B. Vasantha Kandasamy, Florentin Smarandache, N. Suresh Babu, R.S. Selvaraj
The hot category of rank distance m-codes could be helpful within the m-public key m-cryptosystems (m>1) and m-redundant array of cheap disks. AMRD-m-codes can be utilized in info multi (m)-storage structures. those m-codes offer a cheap, time-saving substitute.
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Now we proceed on to define semi MRD bicode. 19: Let C1[n1, k1] be a [n1, k1] RD code and C2[n2, k2, d2] be a MRD code. C1[n1, k1] C2[n2, k2, d2] is defined as the semi MRD bicode if n1 z n2 and k1 z k2 and C1[n1, k1] is only a RD-code and not a MRD code. These bicodes will be useful in application where one set of code never attains the singleton-style bound were as the other code attains the singleton style bound. The special nature of these codes will be very useful in applications were two types of RD codes are used simultaneously.
Thus t m1 (C12 ) t m2 (C 22 ) d t m1 (C11 ) t m2 (C12 ) . 2: For any RD bicode C1 C2 and a pair of positive integers (m1, m2), tm1 (C1 ) tm2 (C2 ) d tm1 1 (C1 ) tm2 1 (C2 ) . Proof: Let S1 V n1 with |S1| = m1 and S2 V n 2 with |S2| = m2, V n1 V n 2 is the rank bispace where S1 S2 is a bisubset of V n1 V n 2 . Now t m1 (C1 ) t m2 (C 2 ) = = max{cov(C1, S1) | S1 max{cov(C2, S2) | S2 max{cov(C1, S1) | S1 max{cov(C2, S2) | S2 t m1 1 (C1 ) t m2 1 (C 2 ) . 3: For any biset of positive integers {n1, m1, k1, K1} {n2, m2, k2, K2}; tm1 [n1 , k1 ] tm2 [n2 , k2 ] d tm1 1[n1 , k1 ] tm2 1[ n2 , k2 ] and tm1 (n1 , K1 ) tm2 (n2 , K 2 ) d tm1 1 (n1 , K1 ) tm2 1 (n2 , K 2 ) .
Let u, v Vn where u = (u1, u2, …, un) and v = (v1, v2, …, vn) with each ui, vi F2n . A fuzzy RD word fu is the fuzzy subset of Vn defined by fu = {(v, fu(v)) | v Vn} where fu(v) is the membership function. , error) is made and q to represent the probability that a rank error occurs so that p + q = 1. Then fu(v) = pn–rqr where r = r(u – v; 2) = ||u – v||. 40: For the unidirectional and asymmetric error models assume q to represent the probability that 1o 0 transition or 0 o 1 transition occurs.