2017/08/30 by Esa V. Vesalainen, Vesalainen, Esa V., Anne-Maria Ernvall-Hytönen +1 · 1 citation
Computer Science · Mathematics · #Benford’s Law and Fraud Detection #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1708.09239
openalex publication_date 2017/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We show that for every ℓ>1, there is a counterexample to the ℓ-modular secrecy function conjecture by Oggier, Solé and Belfiore. These counterexamples all satisfy the modified conjecture by Ernvall-Hytönen and Sethuraman. Furthermore, we provide a method to prove or disprove the modified conjecture for any given ℓ-modular lattice rationally equivalent to a suitable amount of copies of ℤ⊕ √(ℓ) ℤ with ℓ ∈ \3,5,7,11,23\. We also provide a variant of the method for strongly ℓ-modular lattices when ℓ∈ \6,14,15\.