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...

A 4-phase Golay sequence pair of length s ≡ 5 (mod 8) is constructed from a Barker sequence of the same length whose even-indexed elements are prescribed. This explains the origin of the 4-phase Golay seed pairs of length 5 and 13. The construction cannot produce new 4-phase Golay sequence pairs, because there are no Barker sequences of odd length greater than 13. A partial converse to the cons...

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...

Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that g is a xed point free involution. If C is extremal of length a multiple of 24 all the involutions are xed point free, except the Golay Code and eventually putative codes of length 120. Connecting module theoretical properties of a self-dual code C with coding theoretical ones of the subcode C...

Similar to algebraic decoding schemes, the (23, 12, 7) Golay code can be decoded by applying the step-by-step decoding algorithm. In this work, a modified step-by-step algorithm for decoding the Golay code is presented. Logical analysis yielded a simple rule for directly determining whether a bit in the received word is correct. The computational complexity can be reduced significantly using th...

An efficient coset based symbol-by-symbol soft-in/soft-out APP decoding algorithm is presented for the Golay code. Its application in the iterative decoding of concatenated Golay codes is examined.

An efficient coset based symbol-by-symbol soft-in/soft-out APP decoding algorithm is presented for the Golay code. Its application in the iterative decoding of concatenated Golay codes is examined.

The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the three-stage construction of Fiedler, Jedwab and Parker [FJP08] involving multi-dimensional Golay arrays, and a “sum-difference” construction that modifies a result due to Eliahou, Kervaire and Saffari [EKS91]. The existence of 4-phase seed pairs of lengths ...

Golay complementary sequences, often referred to as Golay pairs, are characterised by the property that the sum of their aperiodic autocorrelation functions equals to zero, except for the zero shift. Because of this property, Golay complementary sequences can be utilised to construct Hadamard matrices defining sets of orthogonal spreading sequences for DS CDMA systems of the lengths not necessa...