Pair-Partition Constructions for CPM-Based Quantum LDPC Codes

Koki Okada and Kenta Kasai. Updated July 16, 2026.

This page lists finite CPM-based CSS quantum LDPC codes from pair-partition exponent constraints and links only the per-code files that are uniformly available for all listed instances.

arXiv:2607.14091 GitHub commit 9c2a6f2 SHA-256 manifest Citation

Finite Instances

[[n,k,d]]	girth	(J,L)	P	rate	CPM file
[[472,122,14]]	6	(3,8)	59	0.258	CPM
[[488,126,14]]	6	(3,8)	61	0.258	CPM
[[530,216,12]]	6	(3,10)	53	0.408	CPM
[[590,240,12]]	6	(3,10)	59	0.407	CPM
[[1524,766,14]]	6	(3,12)	127	0.503	CPM
[[3122,1788,16]]	6	(3,14)	223	0.573	CPM
[[276,98,14]]	6	(4,12)	23	0.355	CPM
[[372,130,16]]	6	(4,12)	31	0.349	CPM
[[518,228,16]]	6	(4,14)	37	0.440	CPM
[[574,252,18]]	6	(4,14)	41	0.439	CPM
[[848,430,18]]	6	(4,16)	53	0.507	CPM
[[944,478,>=20]]	6	(4,16)	59	0.506	CPM

Data Format

CPM exponent files

A .cpm file starts with CPM_CSS_V1. The next line gives the instance name, lift size P, row weight L, and the two block-row counts. The following J rows are the exponent array e for H_X, and the next J rows are the exponent array d for H_Z.

CPM_CSS_V1
qc_590_240_12 59 10 3 3
e_00 e_01 ... e_09
e_10 e_11 ... e_19
e_20 e_21 ... e_29
d_00 d_01 ... d_09
d_10 d_11 ... d_19
d_20 d_21 ... d_29

Common format

The same .cpm format is used for both column-weight-three and column-weight-four instances.

J=3 files contain three H_X rows and three H_Z rows.
J=4 files contain four H_X rows and four H_Z rows.

Distance Certification Summary

instance	lower-bound check	upper-bound check
[[472,122,14]]	complete exclusion through weight 12, plus even-weight property	non-stabilizer representatives of weight 14
[[488,126,14]]	complete exclusion through weight 12, plus even-weight property	non-stabilizer representatives of weight 14
[[530,216,12]]	complete exclusion through weight 10, plus even-weight property	non-stabilizer representatives of weight 12
[[590,240,12]]	complete exclusion through weight 10, plus even-weight property	non-stabilizer representatives of weight 12
[[1524,766,14]]	complete exclusion through weight 12, plus even-weight property	non-stabilizer representatives of weight 14
[[3122,1788,16]]	complete exclusion through weight 14, plus even-weight property	non-stabilizer representatives of weight 16
[[276,98,14]]	complete exclusion through weight 12, plus row-family parity	non-stabilizer representatives of weight 14
[[372,130,16]]	complete exclusion through weight 14, plus row-family parity	non-stabilizer representatives of weight 16
[[518,228,16]]	complete exclusion through weight 14, plus row-family parity	non-stabilizer representatives of weight 16
[[574,252,18]]	complete exclusion through weight 16, plus row-family parity	X-side non-stabilizer representative of weight 18
[[848,430,18]]	complete exclusion through weight 16, plus row-family parity	X-side non-stabilizer representative of weight 18
[[944,478,>=20]]	complete X-side exclusion through weight 18, plus verified CSS-side isometry	no upper-bound witness claimed

Construction Files

CPM exponent files

Citation

@unpublished{okadaKasaiPairPartitionCPM2026,
  author = {Koki Okada and Kenta Kasai},
  title  = {Pair-Partition Constructions for CPM-Based Quantum LDPC Codes},
  note   = {Manuscript},
  year   = {2026}
}