SYNTHESIS OF GOLD'S CODE ENSEMBLES FOR USE IN CELLULAR NETWORKS, NAVIGATION AND PULSED RADAR

An algorithm for the synthesis of ensembles of pseudorandom sequences of binary Gold codes is considered using the procedure for the formation of the so-called "paired" m-sequence, which is generated by decimation (thinning) from the corresponding primitive polynomial of degree n, where 5 ≤ n ≤ 10. As a result, an optimal (preferred) pair of m-sequences is formed, which gives rise to one ensemble of the above-mentioned codes. It is shown that there can be a sufficiently large number of such different (for a specific value of the degree of the primitive polynomial n) ensembles, which allows the designer of the corresponding system to change the signature of the used Gold codes according to a random law, while ensuring the required noise immunity of the system. An example of the use of a recurrence algorithm used in cryptography to search for the values of the coefficients of the corresponding primitive polynomial, which is included in the optimal pair of polynomials, according to a known arbitrary continuous fragment of the m-sequence with a length of at least 2×n elements, is proposed and given. Some simplification of this procedure is envisaged due to the use of such a method for determining the coefficients of a primitive polynomial, including its implementation by forming and solving (for example, by the classical Gaussian method, taking into account the peculiarities of trivial binary modular arithmetic) a system of linear equations with coefficients, free terms and unknowns that represent the elements of the Galois field. In addition, the application of the method of formation of a linear system of equations on the basis of the difference recursion equation, together with the above, will provide less computational complexity (for relatively small values of n above) than in the case of using, for such purposes, the well-known Berlekamp-Massey algorithm. Criteria for ordering Gold codes have been proposed, taking into account their correlation properties, as well as a service algorithm in a high-level programming language has been developed for synthesis and selection from a certain ensemble of the required number of Gold codes with the best, depending on the field of their application, correlation properties.