Title :
New Binomial Bent Functions Over the Finite Fields of Odd Characteristic
Author :
Helleseth, Tor ; Kholosha, Alexander
Author_Institution :
Dept. of Inf., Univ. of Bergen, Bergen, Norway
Abstract :
The p-ary function f(x) mapping GF(p4k) to GF(p) and given by f(x)=Tr4k(xp3k+p2k-pk+1+x2) is proven to be a weakly regular bent function and the exact value of its Walsh transform coefficients is found. This is the first proven infinite class of nonquadratic generalized bent functions over the fields of an arbitrary odd characteristic. The proof is based on a few new results in the area of exponential sums and polynomials over finite fields that may also be interesting as independent problems.
Keywords :
Boolean functions; computational complexity; transforms; Walsh transform coefficients; arbitrary odd characteristic; binomial bent functions; finite fields; nonquadratic generalized bent functions; p-ary function mapping; Codes; Computer science; Councils; Cryptography; Finite element methods; Galois fields; Hamming distance; Informatics; Information theory; Polynomials; Transforms; $p$-ary bent function; Walsh transform; polynomial over finite field; root; weakly regular bent function;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2055130
