The t-wise intersection of constant-weight codes are computed.Based on the above result,the t-wise intersection of relative two-weight codes are determined by using the finite geometric structure of relative two-weight codes.
For two odd integers m and s with 1≤s < m and gcd(m, s) = 1, let h satisfy h(2~s-1) ≡1(mod 2~m+ 1) and d =(h + 1)(2~m-1) + 1. The cross correlation function between a binary m-sequence of period 22~m-1 and its d-decimation sequence is proved to take four values, and the correlation distribution is completely determined. Let n be an even integer and k be an integer with 1≤k≤n/2. For an odd prime p and a p-ary m-sequence {s(t)} of period p^n-1, define u(t) =∑(p^k-1)/2 i=0 s(d_it), where d_i = ip^(n/2) + p^k-i and i = 0, 1,...,(p^k-1)/2. It is proved that the cross correlation function between {u(t)} and {s(t)} is three-valued or four-valued depending on whether k is equal to n/2 or not, and the distribution is also determined.
In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).
JIA WenJieZENG XiangYongLI ChunLeiHELLESETH TorHU Lei
Recently, a class of non-primitive cyclic codes with two nonzeros have received much attention of researchers and their weight distributions have been obtained for several cases of two key parameters related to the nonzeros. In this paper, by evaluating certain Jacobi sums, we determine the weight distributions of this class of cyclic codes for one more special case.
