5 papers
Lines in the prime number graph
Scott Duke Kominers, Rudi MrazoviÄ, Carl Pomerance +1
The prime number graph is the set of points where denotes the prime. Let be the minimum number of straight line segments needed to cover the fir…
Perfect codes in weakly metric association schemes
Minjia Shi, Jing Wang, Patrick Solé
The Lloyd Theorem of (Solé, 1989) is combined with the Schwartz-Zippel Lemma of theoretical computer science to derive non-existence results for perfect codes in the Lee metric, N…
Codes and designs in multivariate -polynomial association schemes
Minjia Shi, Jing Wang, Patrick Solé +1
We generalize the fundamental bounds of Delsarte thesis (1973) on codes of given degree and designs of given strength in the new setting of Bannai et al. (2025). We assume the sche…
Second order Recurrences, quadratic number fields and cyclic codes
Minjia Shi, Xuan Wang, Bouazzaoui Zakariae +2
Wall-Sun-Sun primes (shortly WSS primes) are defined as those primes such that the period of the Fibonacci recurrence is the same modulo and modulo This concept has…
The punctured dodecacode is unique
Markus Grassl, Denis Krotov, Lin Sok +1
The punctured dodecacode is an additive -ary code of length and distance which is uniformly packed. We show that a code with the same weight distribution is equivalent…