Method and apparatus for the construction and transmission of binary quasi orthogonal vectors

Abstract

A transmission method in a communications system has an orthogonal code vector for transmitting message signals. A first vector matrix is formed using a first series of cyclic shifts of a sequence having a characteristic polynomial wherein the characteristic polynomial of the sequence is a primitive polynomial having a degree r. A second vector matrix is formed using a second series of cyclic shifts in accordance with whether r is odd or even. The first vector matrix is permuted to provide an orthogonal code. The permuting operations are determined. The determined permuting operations are applied to the second matrix to provide a binary quasi orthogonal code vector. The binary quasi orthogonal code vector is applied to a message signal to provide an encoded message signal for transmission in the communications system. The transmission method also includes forming a vector matrix using a series of cyclic shifts of a sequence having a characteristic polynomial. The characteristic polynomial of the sequence is a primitive polynomial having a degree r. The method further includes permuting the vector matrix to form an orthogonal code to thereby provide a permutation matrix. The permutation matrix is applied to a message signal to provide an encoded message signal and the encoded message signal is transmitted in the communications system.