Complex Golay sequences were introduced in 1992 to generalize constructions for Hadamard matrices using Golay sequences. (In the last section of this paper we describe some independent earlier work on quadriphase pairs–equivalent objects used in the setting of signal processing.) Since then we have constructed some new in7nite classes of these sequences and learned some facts about their struct...

The weighing lysimeters provide scientist the basic information for research related to the evapotranspiration, high quality of the collected data from lysimeters is of great significance. However there are many factors that can affect the measurement accuracy of the weighing lysimeter. In this paper, a data acquisition system was developed to collect the data from 24 weighing lysimeters. The c...

A new proof of the uniqueness and of the existence of the extended ternary Golay code is presented. The proof connects the code to the projective plane of order 3 and is of an elementary nature. The available proofs of the uniqueness of the extended ternary Golay code [2,7] are much more complicated than the standard corresponding proof in the binary case [2]. The prevailing opinion seems to be...

When can one see from the spectrum of a graph whether it is distance-regular or not? We give some new results for when this is the case. As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2, 1), (3, 1) and (4, 1), the Biggs-Smith graph, the M22 graph, and the ...

The extended Golay code is shown to be representable as a chained polar subcode. This enables its decoding with the successive cancellation decoding algorithm and its stack generalization. The decoder can be further simplified by employing fast Hadamard transform. The complexity of the obtained algorithm is comparable with that of the Vardy algorithm.

AbstTactwe present algorithms for maximum likelihood soft decoding of the second order Reed-Muller codes RM(2,m) and the extended (24,12,8) Golay code. The decoding procedures are based on a concise representation of appropriately selected cosets of a subcode of the code considered. Such representation enables application of certain elimination rules. A structure, called constrained design, is ...

In [17] Turyn constructed the famous binary Golay code of length 24 from the extended Hamming code of length 8 (see also [10, Theorem 18.7.12]). The present note interprets this construction as a sum of tensor products of codes and uses it to construct certain new extremal (or at least very good) self-dual codes (for example an extremal doubly-even binary code of length 80). The lattice counter...

Abstmct Two soft-decision algorithms f o r decoding the (6,3,4) q u a t e r n a r y code, the hezocode, are p resented. Both algorithms have the same guaranteed error cor rec t ion radius as that of maximum-likelihood decoding. In using them, bounded-distance decoding of the Golay code and the Leech lattice are performed i n at most 187 and 519 real operations respectively. We present s o m e s...

Definition of the strongly regular graphs on 77 and 100 vertices belonging to the simple groups M22 and HiS.