Binomial p-ary sequences form a basis for the vector space over F_p of all p-ary sequences with period a power of p.
Finite Fields and Their Applications8(2), 256–267 (2002) https://doi
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Binomial sequences over prime fields
Binomial p-ary sequences form a basis for the vector space over F_p of all p-ary sequences with period a power of p.