Sol& P., A. Ghafoor and S.A. Sheikh, The covering radius of Hadamard codes in odd graphs, Discrete Applied Mathe-atics 37/38 (1992) 501-5 10. The use of odd graphs has been proposed as fault-tolerant interconnection networks. The following problem originated in their design: what is the graphical covering radius of an Hadamard code of length 2k1 and siLe 2k1 in the odd graph Ok? Of particular i...

As a continuation of previous work of the first author with S. Ranjbar [26] on a special form of variational inequalities in Hadamard spaces, in this paper we study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudomon...

This paper addresses aspects of channel coding in orthogonal frequency-division multiplexing–code-division multiple access (OFDM-CDMA) uplink systems where each user occupies a bandwidth much larger than the information bit rate. This inherent bandwidth expansion allows the application of powerful low-rate codes under the constraint of low decoding costs. Three different coding strategies are c...

In this paper, we propose a new method to design low-density parity-check Hadamard (LDPC-Hadamard) codes — type of ultimate-Shannon-limit approaching channel codes. The technique is based on applying constraints the check nodes in generalized protograph-based LDPC code, followed by lifting protograph. We name formed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www....

The rigidity of a matrix describes the minimal number of entries one has to change to reduce matrix’s rank to r. We give very simple combinatorial proof of the lower bound for the rigidity of Sylvester (special case of Hadamard) matrix that matches the best known result by de Wolf(2005) for Hadamard matrices proved by quantum information theoretical arguments.

We present the main results on 2PFA’s and on the Hadamard quotient of formal power series, the connection between the two notions being a result stating that the event defined by a 2PFA is the Hadamard quotient of two rational power series.

The trace map has been used very successfully to generate cocyclic complex and Butson Hadamard matrices and simplex codes over Z4 and Z2s . We extend this technique to obtain new linear codes over Zps . It is worth nothing here that these codes are cocyclic but not simplex codes. Further we find that the construction method also gives Butson Hadamard matrices of order p.

In this paper, we give families of self-dual Z4-codes of Type IV-I and Type IV-II generated by conference matrices and skew-Hadamard matrices. Furthermore, we give a family of self-dual Z4-codes of Type IV-I generated by bordered skew-Hadamard matrices.