Arithmetic of finite fields by Charles Small

By Charles Small

Textual content for a one-semester direction on the complex undergraduate/beginning graduate point, or reference for algebraists and mathematicians attracted to algebra, algebraic geometry, and quantity thought, examines counting or estimating numbers of recommendations of equations in finite fields focusing on to

Show description

Read Online or Download Arithmetic of finite fields PDF

Best information theory books

The Problem of Incomplete Information in Relational Databases

In a relational database the knowledge is recorded as rows in tables. even if, in lots of sensible occasions the to be had info is incomplete and the values for a few columns are lacking. but few latest database administration structures permit the consumer to go into null values within the database. This monograph analyses the issues raised via permitting null values in relational databases.

Multimedia Signal Coding and Transmission

This moment quantity covers the theoretical backgrounds and all elements of picture, video and audio compression and expression, dependent via function: colour, Texture, facet research, function aspect and region Detection, Geometry, Contour and form research, Correspondence research, movement research, 3D Scene, Disparity and intensity research, Mosaics, Face Detection and outline, Audio sign beneficial properties in Time and Frequency domain names, Audio constitution and Melody Extraction.

Extra resources for Arithmetic of finite fields

Sample text

Comput. 9 (2), pp. 139–152, 1998. 58. H. Dobbertin. Almost perfect nonlinear power functions over GF (2n ): the Niho case. Inform. , 151, pp. 57–72, 1999. 59. H. Dobbertin. Almost perfect nonlinear power functions over GF (2n ): the Welch case. IEEE Trans. Inform. Theory, 45, pp. 1271–1275, 1999. 60. H. Dobbertin. Almost perfect nonlinear power functions over GF (2n ): a new case for n divisible by 5. Proceedings of Finite Fields and Applications FQ5, pp. 113–121, 2000. 61. H. Dobbertin. Private communication.

We have the following known facts on connection between CCZ-equivalence, isotopisms and strong isotopisms: • two planar DO polynomials F and F are CCZ-equivalent if and only if the corresponding commutative semifields SF and SF are strongly isotopic [22]; • two commutative presemifields of order p n with n odd are isotopic if and only if they are strongly isotopic [44]; • any commutative presemifield of odd order can generate at most two CCZequivalence classes of planar DO polynomials [44]; • if S1 and S2 are isotopic commutative semifields of characteristic p with the order of the middle nuclei and nuclei p m and p k , respectively, then one of the following statements must hold (a) m/k is odd and S1 and S2 are strongly isotopic, (b) m/k is even and either S1 and S2 are strongly isotopic or the only isotopisms between S1 and S2 are of the form (α N, N , L) where α is a non-square element of Nm (S1 ) [44] ; • there exist two commutative semifields of order 36 which are isotopic but not strongly isotopic [111].

Codes Cryptography 66(1–3), pp. 99–109, 2013. 102. A. Pott, Y. Tan, T. Feng, and S. Ling. Association schemes arising from bent functions. Des. , vol. 59, no. 1–3, pp. 319–331, Apr. 2011. 103. O. S. Rothaus. On “bent” functions. J. Combin. Theory Ser. A, vol. 20, no. 3, pp. 300–305, 1976. 104. V. Sidelnikov. On mutual correlation of sequences. Soviet Math. , 12, pp. 197–201, 1971. 105. Y. Tan, A. Pott, and T. Feng. Strongly regular graphs associated with ternary bent functions. J. Combin. Theory Ser.

Download PDF sample

Rated 4.91 of 5 – based on 48 votes