Constructingc-ary Perfect Factors

Constructing c-ary Perfect Factors

A c-ary Perfect Factor is a set of uniformly long cycles whose elements are drawn from a set of size c, in which every possible v-tuple of elements occurs exactly once. In the binary case, i.e. where c = 2, these perfect factors have previously been studied by Etzion, [2], who showed that the obvious necessary conditions for their existence are in fact sufficient. This result has recently been ...

New c-ary Perfect Factors in the de Bruijn Graph

A c-ary Perfect Factor is a collection of uniformly long cycles whose elements are drawn from a set of size c, in which every possible v-tuple of elements occurs exactly once. In the binary case, i.e. where c = 2, these perfect factors have previously been studied by Etzion, [1], who showed that the necessary conditions for their existence are in fact sufficient. This result has recently been e...

Almost p-Ary Perfect Sequences

A sequence a = (a0, a1, a2, · · · , an) is said to be an almost p-ary sequence of period n + 1 if a0 = 0 and ai = ζ bi p for 1 ≤ i ≤ n, where ζp is a primitive p-th root of unity and bi ∈ {0, 1, · · · , p − 1}. Such a sequence a is called perfect if all its out-of-phase autocorrelation coefficients are zero; and is called nearly perfect if its out-of-phase autocorrelation coefficients are all 1...

Nonequivalent q-ary Perfect Codes

On Perfect Domination of q-Ary Cubes

The construction of perfect dominating sets in all binary 2-cubes (r > 3) with the same number of edges along each coordinate direction is performed, thus generalizing the known construction of this for r = 3. However, an adaptation of that construction aiming to perfect dominating sets in the 14-ternary cube with edges along all coordinate directions still fails. 1 Perfect Dominating Sets in B...