A random m-ary leach tree is constructed from a random permutation of 1, . . . , n. A la of large numbers is obtained for the height Hn of these trees by applying the theory of branching random alks . In particular, it is sho n that Ha/log n y in probability as n ---~ oo, here y = y(m) is a constant depending upon m only. Interestingly, as m ---~ 00 , y(m) is asymptotic to 1/log m, the coeffici...

Let q = 3l+2 be a prime power. Maximal designed distances of imprimitive Hermitian dual containing q2-ary narrow-sense (NS) BCH codes of length n = (q 6−1) 3 and n = 3(q 2 −1)(q2 +q+1) are determined. For each given n, non-narrow-sense (NNS) BCH codes which achieve such maximal designed distances are presented, and a series of NS and NNS BCH codes are constructed and their parameters are comput...

We study the class of symmetric [Formula: see text]-ary bands. These are semigroups text] such that is invariant under action permutations and idempotent, i.e., satisfies for all text]. first provide a structure theorem these bands extends classical (strong) semilattice decomposition certain classes introduce concept strong we show exactly semilattices extensions Abelian groups whose exponents ...