Meidl, Wilfried and Sankhadip, Roy and Topuzoğlu, Alev
(2014)
*Enumeration of quadratic functions with prescribed Walsh spectrum.*
IEEE Transactions on Information Theory, 60
(10).
pp. 6669-6680.
ISSN 0018-9448 (Print) 1557-9654 (Online)

Official URL: http://dx.doi.org/10.1109/TIT.2014.2341237

## Abstract

The Walsh transform (f) over cap of a quadratic function f : F-p(n) -> F-p satisfies vertical bar(f) over cap vertical bar epsilon{0, p(n+s/2)} for an integer 0 <= s <= n-1, depending on f. In this paper, quadratic functions of the form F-p,F-n(x) = Tr-n(Sigma(k)(i=0) a(i)x(pt+1)) are studied, with the restriction that a(i) is an element of F-p, 0 <= i <= k. Three methods for enumeration of such functions are presented when the value for s is prescribed. This paper extends earlier enumeration results significantly, for instance, the generating function for the counting function is obtained, when n is odd and relatively prime to p, or when n = 2m, for odd m and p = 2. The number of bent and semibent functions for various classes of n is also obtained.

Item Type: | Article |
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Uncontrolled Keywords: | Quadratic Boolean functions; quadratic p-ary functions; Walsh transform; semi-bent functions; plateaued functions; discrete Fourier transform; self-reciprocal polynomials |

Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |

Depositing User: | Alev Topuzoğlu |

Date Deposited: | 14 Nov 2014 22:32 |

Last Modified: | 02 Aug 2019 12:07 |

URI: | https://research.sabanciuniv.edu/id/eprint/25111 |