Aerospace Instrument-Making Annotation << Back ALGORITHM FOR THE FORMATION OF GMW-SEQUENCES WITH A PERIOD OF N = 4095 IN TELEMETRY INFORMATION TRANSMISSION SYSTEMS V.G. Starodubtsev, D.N. Borodko, V.V. Mishko One of the ways to improve systems for the transmission and processing of telemetry information of space vehicles is the use of signals with an extended spectrum, formed on the basis of pseudo-random sequences with given correlation and structural properties. M-sequences and Gordon-Mills-Welch sequence (GMW) are representatives of pseudo-random sequences possessing a two-level periodic autocorrelation function. GMW-sequences that are formed on the basis of basic M-sequences with the same period have higher structural secrecy, which determines the priority of their use in information transfer systems with increased requirements for confi dentiality. The algorithm for the formation of a complete list of test polynomials of GMW-sequences with a period N = 4095 is developed. A qualitative difference from sequences with a shorter period is the possibility of forming GMW-sequences with different equivalent linear complexity, determined by the degree of the test polynomial hг(x), on the basis of the representation of the extended fi eld GF(212) through fi nite fi elds with double expansion GF[(26)2], GF[(24)3] и GF[(23)4]. In the fi eld GF(212) there are 144 primitive polynomials of the twelfth degree, which when forming the GMW-sequences will act as test polynomials for the basic M-sequences. In the subfi elds GF(26), GF(24) и GF(23) there are six and two primitive polynomials, then for each primitive polynomial of the twelfth power, fi ve and one GMW-sequence for each subfi eld can be formed accordingly. A total of 1008 GMW-sequences with a period of N = 4095 can be synthesized, the equivalent linear complexity of which varies from 24 to 192. At its maximum value, the test polynomial hг(x) is the product of sixteen indivisible polynomials of the twelfth degree. Keywords: pseudo-random sequences, correlation function, fi nite fi elds, indivisible and primitive polynomials, equivalent linear complexity, decimation. Contacts: E-mail: vgstarod@mail.ru, E-mail: denisborodko@yandex.ru, E-mail: vasvasmishko@mail.ru Pp. 03-15.