Further explorations into ternary complementary pairs

Further explorations into ternary complementary pairs

In [R. Craigen, C. Koukouvinos, A theory of ternary complementary pairs, J. Combin. Theory Ser. A 96 (2001) 358–375], we proposed a systematic approach to the theory of ternary complementary pairs (TCPs) and showed how all pairs known then could be constructed using a single elementary product, the natural equivalence relations, and a handful of pairs which we called primitive. We also introduc...

On ternary complementary pairs

Let A = {ao, ... , ae-d, B = {bO, ••• , be-d be two finite sequences of length £. Their nonperiodic autocorrelation function N A,B (s) is defined as: £-1-8 £-1-8 NA,B(S) = L aiai+s + L bibi+s' S = 0, ... , £ 1, i=O i=O where x* is the complex conjugate of x. If NA,B(S) = ° for S = 1, ... , £-1 then A, B is called a complementary pair. If, furthermore, ai, bi E {-I, I}, i = 0, ... , £-1, or, ai,...

Multiplications of ternary complementary pairs

Boolean and ternary complementary pairs

A ternary complementary pair, TCPðn;wÞ; is a pair of ð0;71Þ-sequences of length n with zero autocorrelation and weight w: These are of theoretical interest in combinatorics as well as of practical consequence in coding, transmitting and processing various kinds of signals. When one attempts to construct a TCP of given length and weight, the first thing to decide is where to place the zeros, if ...

An update on primitive ternary complementary pairs

In two recent papers we overhauled the theory of ternary complementary pairs, focusing on questions relating to the possible weights of pairs, and special pairs from which all others can be derived, which we call “primitive.” Of particular interest at this time is a new refinement of the concept of primitivity, which necessitates some revisions to our tables. In this article we report on the st...