Loading [a11y]/accessibility-menu.js
On the Dual of the Coulter-Matthews Bent Functions | IEEE Journals & Magazine | IEEE Xplore

On the Dual of the Coulter-Matthews Bent Functions


Abstract:

For any bent function, it is very interesting to determine its dual function, because the dual function is also bent in certain cases. For k odd and gcd(n, k) = 1, it is ...Show More

Abstract:

For any bent function, it is very interesting to determine its dual function, because the dual function is also bent in certain cases. For k odd and gcd(n, k) = 1, it is known that the Coulter-Matthews bent function f(x) = T r (ax 3k+1/2) is weakly regular bent over F3n, where a ∈ F3n*, and T r (·) : F3n → F3 is the trace function. In this paper, we investigate the dual function of f (x), aiming to determine a universal formula. In particular, for two cases, we determine the formula explicitly: for the case of n = 3t + 1 and k = 2t + 1 with t ≥ 2, the dual function is given by Tr (- x32t+1+3t+1+2/a32t+1+3t+1+1) - x32t+1/a-32t+3t+1 + x2/a-32t+1+3t+1+1); and for the case of n = 3t + 2 and k = 2t + 1 with t≥2,the dual function is given by Tr (-x32t+2+1/a32t+2-3t+1+3 - x2.32t+1+3t+1+1/a32t+2+3t+1+3 + x2/a-32t+2+3t+1+3) As a byproduct, we find two new classes of ternary bent functions with only three terms. Moreover, we also prove that in certain cases f (x) is regular bent.
Published in: IEEE Transactions on Information Theory ( Volume: 63, Issue: 4, April 2017)
Page(s): 2454 - 2463
Date of Publication: 31 January 2017

ISSN Information:

Funding Agency:


References

References is not available for this document.