Pattern sets for Fq-sequences invariant under the continued fraction operator K (the Berlekamp-Massey algorithm)

We show that for all infinite sequences s∈ Fq^ω s ∈ F q ω , two properties are preserved under forward and backward application of the continued fraction operator K (the modified Berlekamp-Massey Algorithm). The first preserved property is that if supp(s)⊂ [r]ₙ supp ( s ) ⊂ [ r ] n , that is, the positions of the nonzero elements of s lie in a certain residue class modulo n , then also supp(K(s))⊂ [r]ₙ supp ( K ( s ) ) ⊂ [ r ] n . The other property applies only to fields with characteristic two: if the sequence consists of symbol pairs (s₂ₙ₋₁,s₂ₙ ( s 2 n - 1 , s 2 n ) with s₂ₙ = α s₂ₙ₋₁ s 2 n = α s 2 n - 1 for a fixed α ∈ F2ᵏ α ∈ F 2 k , for all n∈ N n ∈ N and t:= K(s) t : = K ( s ) , then also t₂ₙ = α t₂ₙ₋₁ t 2 n = α t 2 n - 1</