## Linear recurrence relations over finite fieldsPublished by] Department of Mathematics, University of Bergen, 1966 - Finite fields (Algebra) - 424 pages |

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### Contents

Finite fields | 5 |

Irreducible and primitive polynomials | 11 |

Linear recurrence 1 Feedback shift registers | 18 |

32 other sections not shown

### Common terms and phrases

adders apply arbitrary autocorrelation basic field bigrams binary cycle block characteristic polynomial clearly coefficients combination companion matrix consider coordinate sequences coprime corresponding cp(x cycle of length cycle structure cycles of Q(f deg(f degree denote determined difference cycles difference equation direct sum distribution divisor elements Elspas Example exponent factors field GF[q finite field formula Galois field GF[p GF[q given Golomb ideal impulse response sequence integer invariant under decimation irreducible polynomial isomorphism Laksov least common multiple linear recurrence matrix maximal cycle maximal sequences minimum polynomial modulo multigram nomial nonderogatory notation null sequence null-space number of vectors obtained particular per(f periodic sequences primitive polynomials proof reciprocal polynomial recurrence relation recurring sequence regular sequence residue class residue class ring roots of f(x sequence of Q(f subspaces Table Theorem IV.2 theory total number translation trigrams vector sequence vector space vectors 0,0 Ward Zierler