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Published at December 6

Quadratic Modelings of Syndrome Decoding

cs.CR

math.OC

94A60, 08-08

Released Date: December 6, 2024

Authors: Alessio Caminata¹, Ryann Cartor², Alessio Meneghetti³, Rocco Mora⁴, Alex Pellegrini⁵

Aff.: ¹Università di Genova; ²Clemson University; ³Università di Trento; ⁴CISPA Helmholtz Center for Information Security; ⁵Eindhoven University of Technology

Arxiv: http://arxiv.org/pdf/2412.04848v1

$n$	$k$	$t$	Code Type	# Lin Eqs	# Quad Eqs	# Vars	$d_{\mathrm{reg}}$	SR $d_{\mathrm{reg}}$	SD
8	2	2	Goppa	17	38	24	$\leq 8$	3	2
10	5	4	Random*	20	67	40	$\leq 14$	5	3
16	8	2	Goppa	27	78	48	$\leq 16$	5	3
20	10	5	Random*	35	137	80	$\leq 29$	7	3
30	15	7	Random*	50	207	120	$\leq 44$	10	4
32	12	4	Goppa	57	221	128	$\leq 47$	10	3
32	17	3	Goppa	50	158	96	$\leq 32$	5	4
32	22	2	Goppa	45	158	96	$\leq 32$	7	3
40	20	8	Random*	67	356	160	$\leq 78$	16	5
50	30	5	Random	75	347	200	$\leq 74$	15	4
50	40	4	Random	65	347	200	$\leq 74$	17	4
64	52	2	Goppa	79	318	192	$\leq 64$	14	4
64	40	4	Goppa	93	445	256	$\leq 95$	19	4
64	16	8	Goppa	119	572	320	$\leq 126$	21	4