Kaimin Cheng

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20242026

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math.NT2025

The $3$ -sparsity of $X^{n} - 1$ over finite fields

Kaimin Cheng

Let $q$ be a prime power and $F_{q}$ the finite field with $q$ elements. For a positive integer $n$ , the binomial $X^{n} - 1 \in F_{q} [X]$ is said to be $3$ -sparse over…

math.NT2025

The $3$ -sparsity of $X^{n} - 1$ over finite fields, II

Kaimin Cheng

Let $q$ be a power of $2$ and let $F_{q}$ be the finite field with $q$ elements. For a positive integer $n$ , the polynomial $X^{n} - 1 \in F_{q} [X]$ is called $3$ -sparse ov…

cs.CR2025

Weight distribution of a class of $p$ -ary codes

Kaimin Cheng, Du Sheng

Let $p$ be a prime, and let $N$ be a positive integer such that $p$ is a primitive root modulo $N$ . Define $q = p^{e}$ , where $e = ϕ (N)$ , and let $F_{q}$ be the finite field o…

math.NT2025

Multiplicative character sums over two classes of subsets of quadratic extensions of finite fields

Kaimin Cheng, Arne Winterhof

Let $q$ be a prime power and $r$ a positive even integer. Let $F_{q}$ be the finite field with $q$ elements and $F_{q^{r}}$ be its extension field of degree $r$ . Le…

The 3-sparsity of Xn−1 over finite fields

The 3-sparsity of Xn−1 over finite fields, II

Weight distribution of a class of p-ary codes

Multiplicative character sums over two classes of subsets of quadratic extensions of finite fields

The $3$ -sparsity of $X^{n} - 1$ over finite fields

The $3$ -sparsity of $X^{n} - 1$ over finite fields, II

Weight distribution of a class of $p$ -ary codes