On the trifference problem for linear codes

2021/04/30 by Cosmin Pohoata, Pohoata, Cosmin, Dmitriy Zakharov +1 · 2 citations
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2105.00122

openalex publication_date 2021/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that perfect 3-hash linear codes in \mathbbF₃ⁿ must have dimension at most ((1)/(4)-ε)n for some absolute constant ε> 0.

Cited by

• Polynomially Improved Lower Bounds for Trifferent Codes via Locally Sparse 3-Uniform Hypergraphs
• Vector Trifference

Related

• Bounds on k-hash distances and rates of linear codes
• Polynomially Improved Lower Bounds for Trifferent Codes via Locally Sparse 3-Uniform Hypergraphs
• Trifferent codes with small lengths
• Improved Upper Bound for the Size of a Trifferent Code
• Vector Trifference