Coset Lifted Product Codes: Constructing Quantum LDPC Codes from Non-Normal Subgroup Actions
Abstract
We introduce coset lifted product (CLP) codes, a family of quantum LDPC codes that combine the protograph structure of lifted product codes with the coset action of Aydin, Tamo, and Barg \cite{AydinTamoBarg2026}. Given a finite group G, a subgroup H ≤ G that need not be normal, a protograph A over 𝔽2[G], and a protograph B over 𝔽2[NG(H)], the two protographs act on the cosets G/H from the left and from the right to produce quantum CSS codes. Further, for groups of odd order, we give an explicit formula for the dimension as a sum over the irreducible representations ρ of G of hypergraph product dimensions. A search over $14,843$ pairs (G,H) with H restricted to be non-normal and 120 ≤ n ≤ 400 yields certified codes that exceed the best published value of Q=kd2/n at check weights $6,7$ and $9$, i.e., we obtain $[[360,20,20]]$ at w=6, a $[[360,24,20]]$ code at w=7, and codes $[[252,16,18]]$ and $[[288,16,20]]$ at w=9. Our search also produce high-distance codes with parameters $[[168,10,14]], [[240,8,20]]$ at w=6 and $[[216,8,18]]$ at w=7.
Related
- Graphical Analysis of Lifted Product Code Constructions
- Lifted-Product QLDPC Codes in the Polynomial Domain
- Fast Fault-Tolerant Decoders for Hypergraph Product and Lifted-Product Codes
- Coprime Actions and Characters Non-vanishing on the Fixed-point Subgroup
- Selfless Reduced Crossed Product C*-Algebras Arising from Almost Periodic Actions
BibTeX
@misc{rajpurohit2026coset,
title = {{Coset Lifted Product Codes: Constructing Quantum LDPC Codes from Non-Normal Subgroup Actions}},
author = {Rajendra Prasad Rajpurohit and V. Lalitha and Shayan Srinivasa Garani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12782},
eprint = {2610.12782},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12782},
}
RIS
TY - UNPB
TI - Coset Lifted Product Codes: Constructing Quantum LDPC Codes from Non-Normal Subgroup Actions
AU - Rajendra Prasad Rajpurohit
AU - V. Lalitha
AU - Shayan Srinivasa Garani
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12782
UR - https://arxiv.org/abs/2610.12782
AB - We introduce coset lifted product (CLP) codes, a family of quantum LDPC codes that combine the protograph structure of lifted product codes with the coset action of Aydin, Tamo, and Barg \cite{AydinTamoBarg2026}. Given a finite group G, a subgroup H ≤ G that need not be normal, a protograph A over 𝔽_2[G], and a protograph B over 𝔽_2[N_G(H)], the two protographs act on the cosets G/H from the left and from the right to produce quantum CSS codes. Further, for groups of odd order, we give an explicit formula for the dimension as a sum over the irreducible representations ρ of G of hypergraph product dimensions. A search over $14,843$ pairs (G,H) with H restricted to be non-normal and 120 ≤ n ≤ 400 yields certified codes that exceed the best published value of Q=kd^2/n at check weights $6,7$ and $9$, i.e., we obtain $[[360,20,20]]$ at w=6, a $[[360,24,20]]$ code at w=7, and codes $[[252,16,18]]$ and $[[288,16,20]]$ at w=9. Our search also produce high-distance codes with parameters $[[168,10,14]], [[240,8,20]]$ at w=6 and $[[216,8,18]]$ at w=7.
ER -