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

Abstract We show that for all infinite sequences s Fq^ 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) rₙ 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) ) rₙ supp (K (s) ) ⊂ r n. The other property applies only to fields with characteristic two: if the sequence consists of symbol pairs (s₂₍-₁, s₂₍ (s 2 n - 1, s 2 n) with s₂₍ = s₂₍-₁ s 2 n = α s 2 n - 1 for a fixed F₂㵮 α ∈ F 2 k, for all n N n ∈ N and t: = K (s) t: = K (s), then also t₂₍ = t₂₍-₁ t 2 n = α t 2 n - 1</