We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also correspo...

Sequences with good correlation properties have been widely adopted in modern communications, radar and sonar applications. In this paper, we present our new findings on some constructions of single H-ary Golay sequence and 4-QAM Golay complementary sequence with a large zero autocorrelation zone, where H ≥ 2 is an arbitrary even integer and q ≥ 2 is an arbitrary integer. Those new results on G...

In this paper,we present new constructions for M -QAM and 2M Q-PAM Golay complementary sequences of length 2 for integer n, where M = 2 for integer m. New decision conditions are proposed to judge whether the sequences with offset pairs proposed by Ying Li are Golay complementary, and with the new decision conditions, we prove the conjecture 1 and point out some drawbacks in conjecture 2 propos...

Polynomials in differentiation operators are considered. Joint covariance with respect to Darboux transformations of a pair of such polynomials (Lax pair) as a function of one-field is studied. Methodically, the transforms of the coefficients are equalized to Frechèt differential (first term of the Taylor series on prolonged space) to establish the operator forms. In the commutative (Abelian) c...

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,...

A general decoding method for cyclic codes is presented which gives promise of substantially reducing the complexity of decoders at the cost of a modest increase in decoding time (or delay). Significant reductions in decoder complexity for binary cyclic finite-geometry codes are demonstrated, and two decoding options for the Golay code are presented.

We introduce new techniques to derive compact descriptions of Golay sequences and their extensions. In particular we show how a fundamental notion of commu-tative algebra, namely the notion of Grr obner bases, can be successfully employed to give compact description of Golay sequences. We then concentrate on the practically important case of Golay sequences of length 2 n. For those sequences we...