## Errata (Handbook of Finite Fields)

Last updated: October 5, 2016

- Section 2.1, page 20, Remark 2.1.77, 2nd line: "The set of automorphisms of F
_{q}" should be "The set of automorphisms of F_{qn}".- Section 2.1, page 22, Definition 2.1.92, 1st line: the font of "F" in "be a set of $n$ elements of $\mathbb{F}$ viewed'' should be $F$. The same paragraph, lines 2 and 4, the font of "F" should be $\Delta_{F/K}$.

(Reported on August 13, 2015 by Kaveh Fazli.)

- Section 2.1, page 22, Remark 2.1.99, 2nd line: "alpha
^{q}= (a_{n-1},a_{0},...,a_{n-2})" should be "beta^{q}= (a_{n-1},a_{0},...,a_{n-2})".

(Reported on April 17, 2014 by Jorge Nakahara.)

- Section 2.1, page 23, Remark 2.1.107, last word: "F
_{q}" should be "F_{qn}".

(Reported on August 13, 2015 by Kaveh Fazli.)

- Section 2.1, page 24, Remark 2.1.118: "irreducible" missing; it should be "The roots of any degree $n$ irreducible polynomial over F
_{q}must be in F_{qn}."

(Reported on April 29, 2016 by Gary McGuire.)

- Section 2.2, page 39, Remark 2.2.17, 5th line: "exhastive" should be "exhaustive".
- Section 2.2, page 40, Remark 2.2.18, 14th line: "pver" should be "over".
- Section 2.2, page 48, Table 2.2.11, Mathematica entrance: "concetrating" should be "concentrating".

(Reported on April 17, 2014 by Jorge Nakahara.)

- Section 3.1, page 53, Remark 3.1.1, 4th line: "mutivariate" should be "multivariate".

(Reported on April 17, 2014 by Jorge Nakahara.)

- Section 3.1, page 55, Remark 3.1.11: at the end add the sentence "The simplest expression of the formulae occurs when $n$ is an odd prime.".
- Section 3.1, page 55, Theorem 3.1.12: add the following assumption to the conditions of the theorem: "Suppose also $n$ is an odd prime."

(Reported on December 23, 2015 by Dinesh Thakur.)

- Section 3.1, page 57, Definition 3.1.22: "max(deg(f(x)),deg(g(x)))=2" should be "max(deg(g(x)),deg(h(x)))=2".

(Reported on July 9, 2017 by Fabio Brochero.)

- Section 3.1, page 58, Theorem 3.1.32: this theorem holds only if q is a prime.

(Reported on September 6, 2016 by Lucas Reis.)

- Section 3.2, page 63, Theorem 3.2.31, 3rd line: "polynomial an an irreducible" should be "polynomial and an irreducible".

(Reported on June 9, 2014 by Fabio E. Brochero Martinez.)

- Section 3.3, page 68, Corollary 3.3.30, 3rd line: "has no root" should be "have no root".
- Section 3.3, page 69, Theorem 3.3.41, 1st line: the subscript for the sum should be "i belongs to S" (the symbol for "belongs" is missing).

(Reported on April 17, 2014 by Jorge Nakahara.)

- Section 3.6, page 81, Definition 3.6.14, 1st line: "Def f" should be "Deg f".

(Reported on April 17, 2014 by Jorge Nakahara.)

- Section 4.2, page 91, Definition 4.2.13, 3rd line: "divisor or r" should be "divisor of r".

(Reported on April 17, 2014 by Jorge Nakahara.)

- Section 5.1, page 103, Corollary 5.1.15, 1st line: "basis of of" should be "basis of".

(Reported on April 17, 2014 by Jorge Nakahara.)

- Section 5.3, page 126, Remark 5.3.53, 7th line: "implies that that k" should be "implies that k".

(Reported on April 17, 2014 by Jorge Nakahara.)

- Section 7.2, page 204, Remark 7.2.22: "demote" should be "denote".

(Reported on May 11, 2014 by Jorge Nakahara.)

- Section 9.6, page 283, Theorem 9.6.2, 5th line, below the Waring formula: (i
_{1}, i_{2},..., i_{n}) should be (i_{1}, i_{2},..., i_{k}).

(Reported on Jan 13, 2014 by Donald Richardson.)

- Section 9.6, page 284, Theorem 9.6.12, 3rd line: "Let m
_{d}is the..." should be "Let m_{d}be the...".

(Reported on May 11, 2014 by Jorge Nakahara.)

- Section 9.7, page 291, Proposition 9.7.9, 5th line: "isomorphism off a " should be "isomorphism of a ".
- Section 9.7, page 294, Corollary 9.7.36, 2nd line: "n_{c,f}" should be "n_{f,c}".
- Section 9.7, page 297, Remark 9.7.67, last line: "liesurely" should be "leisurely".

(Reported on May 11, 2014 by Jorge Nakahara.)

- Section 10.5, page 341, Remark 10.5.30: "in an construction" should be "in a construction".

(Reported on May 11, 2014 by Jorge Nakahara.)

- Section 11.6, page 399, Remark 11.6.39, 5th line: "reseachers" should be "researchers".

(Reported on May 11, 2014 by Jorge Nakahara.)

- Section 12.2, page 427, Definition 12.2.26, 1st line: "E
_{1}to to E_{2}" should be "E_{1}to E_{2}".- Section 12.2, page 429, Proposition 12.2.36, 2nd line: "field of characterstic" should be "field of characteristic".

(Reported on May 11, 2014 by Jorge Nakahara.)

- Section 13.2, page 505, Lemma 13.2.31, 1st line: C=circ(c
_{1},...,c_{m}) should be C=circ(c__{0},...,c_{m-1}).

(Reported on June 3, 2014 by Jorge Nakahara.)

- Section 13.2, page 505, Theorem 13.2.37, 4th line: \gamma = \begin{cases}2& \mbox{if $q$ is even,} \cr 1 &\mbox{if $q$ and $n$ are odd.} \end{cases} should be \gamma = \begin{cases}1& \mbox{if $q$ is even,} \cr 2 &\mbox{if $q$ and $m$ are odd.} \end{cases}.
- Section 13.2, page 505, Theorem 13.2.37, 6th line (Formula (13.2.5): q^{s(s-1)/2} should be 2q^{s(s-1)}.

(Reported on September 7, 2016 by Marko Orel.)

- Section 13.2, page 506, Lemma 13.2.38, 1st line: C=circ(c
_{1},...,c_{m}) should be C=circ(c__{0},...,c_{m-1}).

(Reported on June 3, 2014 Jorge Nakahara.)

- Section 13.4, page 522, Definition 13.4.5, 2nd and 3rd lines of item 2: "negate in 3 (resp. 6) boolean operations and double in 0 (resp. 5) boolean operations" should be "negate in 6 (resp. 3) boolean operations and double in 5 (resp. 0) boolean operations".
- Section 13.4, page 522, Table 13.4.1, 2nd line: negation entrance for F
_{5}should be "6" instead of "5".

(Reported on June 3, 2014 by Jorge Nakahara.)

- Section 14.2, page 559, Definition 14.2.42: remove "of" inĀ "every line of is incident".

(Reported on June 3, 2014 by Jorge Nakahara.)

- Section 15.1, page 664, Definition 15.1.46, inside display formula: "({\bf x}, {\bf y}) = i" should be "d({\bf x}, {\bf y}) = i". (Reported on September 10, 2015 by Henry de Valence.)

- Section 16.2, page 759, Definition 16.2.45, last three lines: "where $t=\sigma(y
_{0},..., y_{(\lg w)-1})$, $\lg w$ is the logarithm of $w$ in the base 2, and $\sigma(y_{0},..., y_{(\lg w)-1})$ is the integer representation of binary string $(y_{0},..., y_{(\lg w)-1})$. should be "where $t=\sigma(y_{w-(\lg w)},..., y_{w-1})$, $\lg w$ is the logarithm of $w$ in the base 2, and $\sigma(y_{w-(\lg w)},..., y_{w-1})$ is the integer representation of binary string $(y_{w-(\lg w)},..., y_{w-1})$".- Section 16.2, page 761, Remark 16.2.53, 2nd line: "by the primitive polynomial" should be "by the irreducible polynomial".

(Reported on June 3, 2014 by Jorge Nakahara.)