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Subsequences of Sidelnikov sequences have several desirable cryptographic features such as high linear complexity over 2 and small aperiodic autocorrelation. Here we analyse the k-error linear complexity over  p of subsequences of Sidelnikov sequences of length (q –1)/3. The proofs are based on results on equations with binomial coefficients modulo p partly obtained using character sum techniques.

𝑘-error linear complexity over 𝔽 p of subsequences of Sidelnikov sequences of period (pr – 1)/3