problems/covering/share/2026-08-16/result/data/H_r18_n815.txt

files / problems / covering / share / 2026-08-16 / result / data / H_r18_n815.txt
# Construction QM_2^2 (arXiv:2511.02542 Theorem 4.1, eq. (4.2),
# (4.4)) applied to the [50,40]_2 2 seed with m = 4.
#
#   H_C = [ D  A(h_1,b_1) ... A(h_50,b_50) ],
#   A(h_j,b_j) columns = (h_j, xi, b_j*xi)^tr, xi over F_{2^4},
#   D = D_1(2): columns (0_10, 0_4, w)^tr, w over nonzero 4-bit
#   vectors (the Hamming parity check matrix W_4).
#
# GF(2^4) modulus 0x13.  r = 10 + 2*4 = 18, n = 2^4 * 51 - 1 = 815.
# LSB-first: bit k of the integer encoding is row k+1.
# Rows 1..10 carry h_j, rows 11..14 carry xi, rows 15..18 carry b_j*xi.
#
# 18 rows, 815 columns; space separated.
# Generated by verify/build_propagation.py -- do not edit by hand.
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