Self-Dual Hadamard Bent Sequences

A new notion of bent sequence related to Hadamard matrices was introduced recently,motivated by a security application(Solé,et al.,2021).The authors study the self-dual class in length at most 196.The authors use three competing methods of generation:Exhaustion,Linear Algebra and Gr?bner bases.Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples.The authors conjecture that if v is an even perfect square,a self-dual bent sequence of length v always exists.The authors introduce the strong automorphism group of Hadamard matrices,which acts on their associated self-dual bent sequences.The authors give an efficient algorithm to compute that group.

Blind recognition of k/n rate convolutional encoders from noisy observation

Blind recognition of convolutional codes is not only essential for cognitive radio, but also for non-cooperative context. This paper is dedicated to the blind identification of rate k/n convolutional encoders in a noisy context based on Walsh-Hadamard transformation and block matrix (WHT-BM). The proposed algorithm constructs a system of noisy linear equations and utilizes all its coefficients to recover parity check matrix. It is able to make use of fault-tolerant feature of WHT, thus providing more accurate results and achieving better error performance in high raw bit error rate (BER) regions. Moreover, it is more computationally efficient with the use of the block matrix (BM) method. ? 2017 Beijing Institute of Aerospace Information.

On a Fast p-ary m-Sequence Transform

m-Sequences have been used widely in many applications, but the corresponding computation of the correlation-detection is overwhelming N2 operations, where N is the length of the m-sequence, such that it is unpractical. In this paper, a transform from p-ary m-sequence matrices to generalized Hadamard matrices is developed; and then by the fast generalized Hadamard matrices transform, a fast p-ary m-sequence transform is developed. The results show that the computation can be dramatically reduced from N2 to Nlog pN operations, so the fast p-ary m-sequence transform could enable a rapid correlation-detection at the receiver.

On Addition of Sets in Boolean Space

In many problems of combinatory analysis, operations of addition of sets are used (sum, direct sum, direct product etc.). In the present paper, as well as in the preceding one [1], some properties of addition operation of sets (namely, Minkowski addition) in Boolean space Bn are presented. Also, sums and multisums of various “classical figures” as: sphere, layer, interval etc. are considered. The obtained results make possible to describe multisums by such characteristics of summands as: the sphere radius, weight of layer, dimension of interval etc. using the methods presented in [2], as well as possible solutions of the equation X+Y=A, where , are considered. In spite of simplicity of the statement of the problem, complexity of its solutions is obvious at once, when the connection of solutions with constructions of equidistant codes or existence the Hadamard matrices is apparent. The present paper submits certain results (statements) which are to be the ground for next investigations dealing with Minkowski summation operations of sets in Boolean space.