Abstract
Let q be a prime power and Fq the finite field with q elements. In this paper, it is shown that the minimal polynomial of a modified de Bruijn sequence of order n over Fq cannot be the product of an irreducible polynomial of degree n over Fq and any polynomial of degree k over Fq if n≥4k, which in fact improves several previous results ([5,13]). Based on this result, a non-trivial lower bound 5n/4 is given for linear complexities of modified de Bruijn sequences of order n distinct from m-sequences, which is the first non-trivial lower bound with no restriction on n.
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