Mathematical proof note · Version 1.0 · October 8, 2026
Strict Nonbinary Rate Bounds Beyond Optimized Classical and Mixed-Channel Envelopes
National Mobile Communications Research Laboratory and the Frontiers Science Center for Mobile Information Communication and Security, Southeast University, Nanjing 211189, China
Abstract
For every fixed integer alphabet size q ≥ 3, we strictly improve the joint flagged envelope of the full-domain Aaltonen/product/shortening family specified here and the unmasked q-ary mixed-channel family near the Plotkin endpoint. Cyclic Gram channels represent the classical envelope exactly. Conditional support expansion improves boundary generators, while independent coherence variations improve full-rank mixed-channel generators outside a finite stationary set. A positive information slope for the remaining generators forces every sufficiently low-rate optimizer to contain an improvable component. The improved channels have output dimension at most 2q^2+q, and the resulting rate bound applies to linear and nonlinear codes.
Full text and source
Keywords
nonbinary codes; asymptotic coding rate bounds; Aaltonen bound; mixed-channel bounds; Plotkin endpoint; classical-quantum channels.
中文关键词：非二元码；渐近码率上界；Aaltonen界；混合信道界；Plotkin端点；经典量子信道。
Suggested citation
S. Yang, "Strict Nonbinary Rate Bounds Beyond Optimized Classical and Mixed-Channel Envelopes," mathematical proof note, version 1.0, Oct. 8, 2026. [Online]. Available: https://github.com/stalin1943/Coding-Theory-Proof-Notes/blob/main/qary-strict-rate-bounds/proof.pdf