Abstract
The article presents the analysis of the linear complexity of periodic q-ary sequences when changing k of their terms per period. Sequences are formed on the basis of new generalized cyclotomy modulo equal to the degree of an odd prime. There has been obtained a recurrence relation and an estimate of the change in the linear complexity of these sequences, where q is a primitive root modulo equal to the period of the sequence. It can be inferred from the results that the linear complexity of these sequences does not sign ificantly decrease when k is less than half the period. The study summarizes the results for the binary case obtained earlier.
Highlights
The article presents the analysis of the linear complexity of periodic q-ary sequences when changing k of their terms per period
Sequences are formed on the basis of new generalized cyclotomy modulo equal to the degree of an odd prime
There has been obtained a recurrence relation and an estimate of the change in the linear complexity of these sequences, where q is a primitive root modulo equal to the period of the sequence. It can be inferred from the results that the linear complexity of these sequences does not sign ificantly decrease when k is less than half the period
Summary
В этом разделе напомним определение q -ичных последовательностей из [15]. Пусть p – простое число, отличное от двух, p = ef +1, где e, f – целые положительные числа, и g – примитивный корень по модулю pn [16]. Согласно [10], обобщенные циклотомические классы порядка d j по модулю p j определяются следующим образом:. На основе этих классов в [11] сформировано новое семейство почти сбаланисированных бинарных последовательностей, их линейная сложность изучена в [3, 11, 12], когда f – четное. J =1 k k = 0, 1, ..., q −1, m =1, 2, ..., n, где q | f , b : 0 ≤ b < pn−1 f и rj = p j−1 f / q
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