2025/02/20 by Coble, Nolan J., Barg, Alexander
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2502.14746
Binary Reed-Muller (RM) codes are defined via evaluations of Boolean-valued functions on ℤ2m. We introduce a class of binary linear codes that generalizes the RM family by replacing the domain ℤ2m with an arbitrary finite Coxeter group. Like RM codes, this class is closed under duality, forms a nested code sequence, satisfies a multiplication property, and has asymptotic rate determined by a Gaussian distribution. Coxeter codes also give rise to a family of quantum codes for which transversal diagonal Z rotations can perform non-trivial logic.