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cs.IT2026
Comments on the recent improvements of the MRRW bounds
Alexander Barg
The asymptotic McEliece--Rodemich--Rumsey--Welch bound (1977) limits the largest attainable rate of binary codes as a function of the relative distance. After a nearly half-century…
cs.IT2026
Universally optimal (wiretap) codes
Madhura Pathegama, Alexander Barg
Universally optimal (UO) codes were introduced by H. Cohn and A. Kumar in 2007 and later extended to the discrete setting by Cohn and Y. Zhao. They minimize the ``energy'' among al…
cs.IT2026
Minimum distance and decoding of Coxeter codes
Alexander Barg, Qëndrim R. Gashi, Tianyuan Xu
A binary Coxeter code associated with a finite Coxeter system is an -linear span of indicators of standard cosets of a fixed rank. Coxeter codes, introduced…