An explicit formula for rank r_n(t) of Gram matrices from m-sequences is derived, proving full rank for about half of admissible t values, with rank-deficient states strictly unstable and full-rank states persistent, completely determining hull distributions of punctured cyclic simplex codes.
Niederreiter,A combinatorial approach to probabilistic results on the linear complexity pro- file of random sequences, J
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Rank Distribution and Dynamics of Gram Matrices from Binary m-Sequences with Applications to LCD Codes
An explicit formula for rank r_n(t) of Gram matrices from m-sequences is derived, proving full rank for about half of admissible t values, with rank-deficient states strictly unstable and full-rank states persistent, completely determining hull distributions of punctured cyclic simplex codes.