Generalised Complementary Arrays

New complementary sets of length $2^m$ and size 4

“…In this paper, we propose constructions for complementary 4-sets instead of complementary pairs, having a very simple graphical description and with pairwise Hamming distance ≥ 2 n−2 . We show how this is a special case of the general array construction given in [8], and clarify aspects of section 5 of [10]. Our construction also generalizes a more explicit construction in [8].…”

“…We show how this is a special case of the general array construction given in [8], and clarify aspects of section 5 of [10]. Our construction also generalizes a more explicit construction in [8]. Lower and upper bounds on the number of sequences generated are analyzed.…”

“…Fiedler, Jedwab, and Parker [4] proposed a matrix framework for constructions of Golay sequences. [5,[8][9][10] show that the complementary set construction is primarily an array construction, where sequence sets are obtained by considering suitable projections of the arrays. It is desirable to propose constructions that significantly improve code rate without greatly compromising the upper bound on PMEPR or pairwise distance.…”

“…Lower and upper bounds on the number of sequences generated are analyzed. Some generalizations of the construction are also given, which are not in the construction given in [8].…”

A complementary construction using mutually unbiased bases

“…The work was subsequently extended by [22,26,27] and by numerous other authors [31]. [19,20,17,10,15,21] show that the complementary set construction is primarily an array construction, where sequence sets are obtained by considering suitable projections of the arrays. It is desirable to propose complementary constructions that significantly improve set size without greatly compromising the upper bound on PAPR or the pairwise distinguishability.…”