16 papers
Additive decompositions of multiplicative subgroups in prime fields: a self-contained approach
Chi Hoi Yip, Semin Yoo
Sárközy conjectured that the nonzero quadratic residues modulo a sufficiently large prime have no nontrivial additive decomposition. Hanson and Petridis proved the conjecture for…
Multiplicative subgroups are not restricted sumsets
Chi Hoi Yip, Semin Yoo
We determine exactly which proper multiplicative subgroups of a prime field can be represented as a restricted sumset of the form $A\mathbin{\widehat{+}} A=\{a+a':a,a'\in A,\ a\ne…
Extensions of the Carlitz-McConnel and Blokhuis-Sziklai theorems for unions of cyclotomic classes
Maosheng Xiong, Chi Hoi Yip
Let be a prime, let , and let . A celebrated result of Carlitz and McConnel states that if is a proper subgroup of ,…
-Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
We investigate -Diophantine sets over finite fields via new explicit constructions of families of quasi-random hypergraphs from multivariate polynomials. In particular, our cons…
On generalized covering radii of binary primitive double-error-correcting BCH codes
Maosheng Xiong, Chi Hoi Yip
The generalized covering radii (GCR) of linear codes are a fundamental higher-dimensional extension of the classical covering radius. While the second and third GCR of binary primi…
Multiplicative irreducibility of shifted multiplicative subgroups
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
In a recent breakthrough, Kalmynin resolved conjectures of Lev--Sonn and Sárközy on additive decompositions of multiplicative subgroups of prime fields. In this paper, inspired by…