#coding theory
4 resultsGraphs related to $2$-dimensional simplex codes
Mariusz Kwiatkowski, Mark Pankov
The paper characterizes the distance structure of the graph formed by 4‑ary simplex codes of dimension 2, showing it is connected with diameter 3 and detailing the vertices at each…
Private Proximity Retrieval Codes
Yiwei Zhang, Eitan Yaakobi, Tuvi Etzion
The paper introduces private proximity retrieval (PPR) schemes that let a user find all database records within a given Hamming distance while keeping a fraction of the user’s reco…
Constructive asymptotic bounds of locally repairable codes via function fields
Liming Ma, Chaoping Xing
The paper presents an explicit asymptotic construction of locally repairable codes over any finite field using local expansions of functions at a rational place, achieving a Tsfasm…
A lower bound on permutation codes of distance $n-1$
Sergey Bereg, Peter Dukes
The paper extends a classic recursive method for constructing mutually orthogonal latin squares to a broader class of permutation codes with length n and minimum distance n‑1, and…