Truth tables of low Hamming weight 1st-order correlation immune Boolean functions with 12 variables

Abstract The dataset comprises two components: (1) 52,339 12-variable, 1st-order correlation immune Boolean functions with weight 256 (2⁸), and (2) 141,893 12-variable, 1st-order correlation immune Boolean functions with weights ranging from 222 to 256. Both sets were generated using the OIWR algorithm. Each line represents one Boolean function by its truth table. Instructions: Mesnager and Su's 2021 work (DOI: 10.1109/TIT.2021.3109946 ) presents a low Hamming weight 1st-order correlation immune Boolean function construction method constrained to weights that are powers of 2. We extend these results using the OIWR algorithm (https://eprint.iacr.org/2026/985), achieving two significant advances: (1) generating multiple Boolean functions under identical constraints, and (2) breaking the power-of-two weight limitation. Our dataset provides truth tables for the special case of 12-variable, weight-256, 1st-order correlation immune Boolean functions, comprising: 1. "12_256_1.txt": 52,339 truth tables (one per line), each representing a distinct 12-variable, weight-256 (2⁸), 1st-order correlation-immune Boolean function.2. "12_(222-256)_1.txt": 141,893 truth tables (one per line) representing 12-variable, 1st-order correlation-immune functions with weights spanning 222-256, distributed as shown in Table: Weight Count Weight Count 222 40 232 19,943 226 1,257 236 28,852 230 10,947 228 4,246 234 27,668 224 258 238 22,914 240 14,717 242 6,478 220 5 244 3,352 246 717 248 432 252 43 250 23 256 1