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In this paper, we make some progress towards a well-known conjecture on the minimum weights of binary cyclic codes with two primitive nonzeros. We also determine the Walsh spectrum of $Tr(x^d)$ over $F_{2^{m}}$ in the case where $m=2t$, $d=3+2^{t+1}$ and $gcd(d, 2^{m}-1)=1$.
The distance distribution of a code is the vector whose $i^text{th}$ entry is the number of pairs of codewords with distance $i$. We investigate the structure of the distance distribution for cyclic orbit codes, which are subspace codes generated by
We study orbit codes in the field extension ${mathbb F}_{q^n}$. First we show that the automorphism group of a cyclic orbit code is contained in the normalizer of the Singer subgroup if the orbit is generated by a subspace that is not contained in a
We consider $q$-ary (linear and nonlinear) block codes with exactly two distances: $d$ and $d+delta$. Several combinatorial constructions of optimal such codes are given. In the linear (but not necessary projective) case, we prove that under certain
We classify 8-divisible binary linear codes with minimum distance 24 and small length. As an application we consider the codes associated to nodal sextics with 65 ordinary double points.
Let $q=2^n$, $0leq kleq n-1$, $n/gcd(n,k)$ be odd and $k eq n/3, 2n/3$. In this paper the value distribution of following exponential sums [sumlimits_{xin bF_q}(-1)^{mathrm{Tr}_1^n(alpha x^{2^{2k}+1}+beta x^{2^k+1}+ga x)}quad(alpha,beta,gain bF_{q})]