86 citations · 421 across the 84 of their papers we have counts for
9 papers · 1 filter
On the proximity of large primes
Minjia Shi, Florian Luca, Patrick Solé
By a sphere-packing argument, we show that there are infinitely many pairs of primes that are close to each other for some metrics on the integers. In particular, for any numeratio…
On self-dual four circulant codes
Minjia Shi, Hongwei Zhu, Patrick Sole
Four circulant codes form a special class of -generator, index , quasi-cyclic codes. Under some conditions on their generator matrices they can be shown to be self-dual. Arti…
Two-weight codes and second order recurrences
Minjia Shi, Zhongyi Zhang, Patrick Sole
Cyclic codes of dimension over a finite field are shown to have at most two nonzero weights. This extends a construction of Rao et al (2010) and disproves a conjecture of Schmi…
Pisano period codes
Minjia Shi, Zhongyi Zhang, Patrick Sole
The cyclic codes with parity check polynomial the reciprocal of the characteristic polynomial of the Fibonacci recurrence over a prime finite field are shown to have either one wei…
Asymptotically Good Additive Cyclic Codes Exist
Minjia Shi, Rongsheng Wu, Patrick Sole
Long quasi-cyclic codes of any fixed index have been shown to be asymptotically good, depending on Artin primitive root conjecture in (A. Alahmadi, C. Güneri, H. Shoaib, P. So…
On self-dual negacirculant codes of index two and four
Minjia Shi, Qian Liqin, Patrick Sole
In this paper, we study a special kind of factorization of over with a prime power when with …
Two weight -codes, odd prime
MinJia Shi, Zahra Sepasdar, Rongsheng Wu +1
We show that regular homogeneous two-weight -codes where is odd and with dual Hamming distance at least four do not exist. The proof relies on…
Constructions of optimal LCD codes over large finite fields
Lin Sok, Minjia Shi, Patrick Solé
In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields…
New Classes of -ary Few Weights Codes
Minjia Shi, Rongsheng Wu, Liqin Qian +2
In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p}…