Let E1 be the near hexagon on 729 points related to the extended ternary Golay code. We prove in an entirely geometricway that the generating and embedding ranks ofE1 are equal to 24. We also study the structure of the universal embeddinge of E1. More precisely, we consider several nice subgeometries A of E1 and determine which kind of embeddingeA is, whereeA is the embedding of A induced by...

Coding theory is the subject which is concerned with how information can be sent over a noisy channel. A code then is a collection of codewords which are strings of a fixed number of letters from an alphabet. Some of these strings are codewords others are not. When a codeword is sent over a channel there is a probability less than /2 that each letter in the codeword will be changed, thus introd...

A blind signature scheme is a cryptographic protocol to obtain a valid signature for a message from a signer such that signer’s view of the protocol can’t be linked to the resulting message signature pair. This paper presents blind signature scheme using Chebyshev polynomials. The security of the given scheme depends upon the intractability of the integer factorization problem and discrete loga...

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it...

Recently Golay complementary sets were shown to exist in the subsets of second-order cosets of a q-ary generalization of the first-order Reed–Muller (RM) code. We show that mutually orthogonal Golay complementary sets can also be directly constructed from second-order cosets of a q-ary generalization of the first-order RM code. This identification can be used to construct zero correlation zone ...

Automorphisms of order 2p in binary self-dual extremal codes of length a multiple of 24 Abstract Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that g p is a fixed point free involution. If C is extremal of length a multiple of 24 all the involutions are fixed point free, except the Golay Code and eventually putative codes of length 120. Conne...

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...

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...