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This book is dedicated to the memory of Florentin Smarandache, who listed many new and unsolved problems in number theory.
The results of this paper are concerned with the multi-covering radius, a generalization of covering radius, of Rank Distance (RD) codes. This leads to greater understanding of RD codes and their distance properties. Results on multi-covering radii of RD codes under various constructions are given by varying the parameters. Some bounds are established. A… (More)
The pair (GH , ·) is called a special loop if (G, ·) is a loop with an arbitrary subloop (H, ·) called its special subloop. A special loop (GH , ·) is called a second Smarandache Bol loop (S 2 nd BL) if and only if it obeys the second Smarandache Bol identity (xs · z)s = x(sz · s) for all x, z in G and s in H. The popularly known and well studied class of… (More)
In this paper we analyze and study the Smarandache idempotents (S-idempotents) in the ring Zn and in the group ring ZnG of a finite group G over the finite ring Zn. We have shown the existance of Smarandache idempotents (S-idempotents) in the ring Zn when n = 2 m p (or 3p), where p is a prime > 2 (or p a prime > 3). Also we have shown the existance of… (More)
— Rosenbloom and Tsfasman introduced a new metric (RT metric) which is a generalization of the Hamming metric. In this paper we study the distance graphs of spaces Z n q and Sn with Rosenbloom-Tsfasman metric. We also describe the degrees of vertices, components and the chromatic number of these graphs. Distance graphs of general direct product spaces also… (More)
The study of zero-divisors in group rings had become interesting problem since 1940 with the famous zero-divisor conjecture proposed by G.Higman . Since then several researchers [1, 2, 3] have given partial solutions to this conjecture. Till date the problem remains unsolved. Now we introduce the notions of Smarandache zero divisors (S-zero divisors) and… (More)