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Locally testable codes, i.e., codes where membership in the code is testable with a constant number of queries, have played a central role in complexity theory. It is well known that a code must be a "low-density parity check" (LDPC) code for it to be locally testable, but few LDPC codes are known to be locally testable, and even fewer classes of LDPC codes are known not to be locally testable. Indeed, most previous examples of codes that are not locally testable were also not LDPC. The onlydoi:10.1109/ccc.2011.14 dblp:conf/coco/Ben-SassonMSS11 fatcat:hks5whha65azvkxlbjfrpse5le