A method for demonstrating and enumerating uniformly efficient (permutation-optimal) trellis decoders for self-dual codes of high minimum distance is developed. Such decoders and corresponding permutations are known for relatively few codes. The task of finding such permutations is shown to be substantially simplifiable in the case of self-dual codes in general, and for self-dual codes of suffi...

It is shown that the codewords of binary and ternary Golay codes can be converted into rays in ${\mathbb{RP}}^{23}$ ${\mathbb{RP}}^{11}$ provide proofs Kochen-Specker theorem real state spaces dimensions 24 12, respectively. Some implications these results are discussed.

We show that the binary Golay code is slightly more power efficient than the extended binary Golay code under maximum-likelihood (ML), hard-decision decoding. In fact, if a codeword from the extended code is transmitted, one cannot achieve a higher probability of correct decoding than by simply ignoring the 24th symbol and using an ML decoder for the non-extended code on the first 23 symbols. T...

A new decoder is proposed to decode the (23, 12, 7) binary Golay-code up to five errors. It is based on the algorithm that can correct up to four errors for the (24, 12, 8) extended Golay-code proposed by Lin et al., thereby achieving the soft decoding in the real sense for the Golay-code. For a weight-2 or weight-3 error pattern decoded by the hard decoder for correcting up to three errors, on...

Identifying binary sequences {} whose autocorrelations {} are jointly as small as possible, for fixed , is important for engineering design purposes. The “best” sequences are those with the largest merit factor  . As an example, the sequence 1−1 1−1 1 1−1−1 1 1 1 1 1 has the largest  value 16912 = 140833 among all such with  = 12. As another example, the sequence 1−1 ...

Article history: Received 5 May 2009 Received in revised form 29 June 2013 Accepted 31 July 2013 Available online 8 August 2013

The main objective of this study is to improve the ultrasound image by employing a new algorithm based on transducer array element beam pattern correction implemented in the synthetic transmit aperture (STA) method combined with emission of mutually orthogonal complementary Golay sequences. Orthogonal Golay sequences can be transmitted and received by different transducer elements simultaneousl...

power, envelope, OFDM, Reed-Muller, code, Golay, complementary, sequence, pair, set Practical communications engineering is continuously producing problems in interest to the coding theory community. A recent example is the power-control problem in Orthogonal Frequency Division Multiplexing (OFDM). We report recent work which gives a mathematical framework for generating solutions to this notor...