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9.4674 0 0 10.3 254.37 241.39 Tm (16 )Tj 0.0402 Tc 9.5 0 0 9.5 267.2 241.39 Tm (are )Tj 0.0412 Tc 1.726 0 Td (Type )Tj 0.0308 Tc 2.597 0 Td (II )Tj -0.0084 Tc 1.097 0 Td (codes, )Tj 0.023 Tc 2.936 0 Td (and )Tj -0.0111 Tc -34.639 -1.194 Td (so )Tj 0.0232 Tc 1.263 0 Td (have )Tj 0.0028 Tc 2.331 0 Td (weight )Tj 0.0378 Tc 3.136 0 Td (enumerator )Tj /T1_1 1 Tf 0 Tc 9.8 0 0 9.8 131.41 230.05 Tm (W)Tj 10 0 0 10 140.35 228.61 Tm (n)Tj 0.733 0.144 Td (. )Tj /T1_0 1 Tf 0.0346 Tc 9.5 0 0 9.5 32.18 218.53 Tm (Based )Tj 0.0057 Tc 2.951 0 Td (on )Tj 0.05 Tc 9.6991 0 0 9.5 73.24 218.53 Tm (the )Tj 0.0126 Tc 9.5 0 0 9.5 89.54 218.53 Tm (above )Tj 0.014 Tc 2.814 0 Td (results, )Tj -0.035 Tc 8.7957 0 0 9.5 148.31 218.53 Tm (we )Tj -0.0021 Tc 9.5 0 0 9.5 161.81 218.53 Tm (have )Tj 0.05 Tc 9.5625 0 0 9.5 183.22 218.53 Tm (the )Tj -0.0133 Tc 9.5 0 0 9.5 199.34 218.53 Tm (following. )Tj 0.05 Tc 10.8409 0 0 9.6 17.76 196.57 Tm (Lemma )Tj 9.6011 0 0 9.6 57 196.57 Tm (2.2 )Tj /T1_1 1 Tf -0.0032 Tc 9.6 0 0 9.6 76.48 196.57 Tm (There )Tj 0.0055 Tc 2.825 0 Td (exist )Tj -0.0128 Tc 2.254 0 Td (pure )Tj -0.035 Tc 9.5571 0 0 9.6 146.83 196.57 Tm (double )Tj 0.0056 Tc 9.6 0 0 9.6 175.79 196.57 Tm (circulant )Tj 0.0042 Tc 4.06 0 Td (self-dual )Tj -0.0263 Tc 3.965 0 Td (codes )Tj 0.0088 Tc 2.643 0 Td (over )Tj /T1_0 1 Tf -0.035 Tc 7.0688 0 0 9.3 298.74 196.57 Tm (lF2 )Tj /T1_2 1 Tf 0 Tc 12.2 0 0 12.2 311.02 196.57 Tm (+ )Tj /T1_1 1 Tf -0.035 Tc 8.1514 0 0 9.6 320.33 196.57 Tm (ulF)Tj 0 Tc 6.5001 0 0 6.5001 331.35 195.13 Tm (2 )Tj -0.023 Tc 9.6 0 0 9.6 339.26 196.57 Tm (which )Tj -0.035 Tc 9.4799 0 0 9.6 18.48 185.05 Tm (are )Tj 0.0446 Tc 9.6 0 0 9.6 34.87 185.05 Tm (not )Tj -0.0069 Tc 1.737 0 Td (the )Tj 0.0159 Tc 1.63 0 Td (inverse )Tj -0.0218 Tc 3.424 0 Td (Gray )Tj 0.0008 Tc 2.397 0 Td (map )Tj -0.0156 Tc 2.129 0 Td (image )Tj 0.0494 Tc 2.798 0 Td (of )Tj 0.0074 Tc 1.145 0 Td (binary )Tj -0.019 Tc 3.003 0 Td (pure )Tj -0.026 Tc 2.23 0 Td (double )Tj 0.0127 Tc 3.054 0 Td (circulant )Tj -0.0051 Tc 4.098 0 Td (self-dual )Tj -0.035 Tc 9.2445 0 0 9.6 336.89 185.05 Tm (codes. )Tj /T1_0 1 Tf 0.05 Tc 15.2958 0 0 13.6 18.11 153.37 Tm (References )Tj -0.035 Tc 7.9767 0 0 9.5 23.03 132.49 Tm ([1] )Tj 9.4252 0 0 9.5 38.24 132.49 Tm (C. )Tj 0.0091 Tc 9.5 0 0 9.5 50.18 132.49 Tm (Bachoc, )Tj 0.0273 Tc 3.678 0 Td (Application )Tj -0.0168 Tc 5.298 0 Td (of )Tj 0.0095 Tc 1.042 0 Td (coding )Tj 0.0356 Tc (theory )Tj 0.0211 Tc 6.108 0 Td (to )Tj 0.0449 Tc 1.118 0 Td (the )Tj 0.0386 Tc 1.66 0 Td (construction )Tj 0.0211 Tc 5.703 0 Td (of )Tj 0.0331 Tc 1.068 0 Td (modular )Tj 0.0129 Tc 3.821 0 Td (lattices, )Tj /T1_2 1 Tf -0.035 Tc 8.8742 0 0 9.1 38.45 120.96 Tm (J. )Tj /T1_1 1 Tf 0.0381 Tc 9.3 0 0 9.3 49.32 120.96 Tm (Com )Tj 0.0012 Tc 2.063 0 Td (bin. )Tj /T1_0 1 Tf 0.0362 Tc 9.5 0 0 9.5 87.4 120.96 Tm (Tbeory )Tj -0.0106 Tc 3.363 0 Td (Ser. )Tj /T1_1 1 Tf 0 Tc 9.3 0 0 9.3 138.2 120.96 Tm (A )Tj /T1_0 1 Tf 0.0288 Tc 9.5 0 0 9.5 148.04 120.96 Tm (78 )Tj -0.0056 Tc 10.3 0 0 10.3 162.06 120.96 Tm (\(1997\),92-119. )Tj -0.035 Tc 7.9767 0 0 9.5 23.21 101.17 Tm ([2] )Tj 9.4347 0 0 9.5 38.3 101.17 Tm (K. )Tj 0.0284 Tc 9.5 0 0 9.5 51.08 101.17 Tm (Betsumiya, )Tj 0.0264 Tc 5.149 0 Td (T.A. )Tj 0.0057 Tc 2.328 0 Td (Gulliver )Tj 0.0419 Tc 3.695 0 Td (and )Tj -0.035 Tc 9.2186 0 0 9.5 175.28 101.17 Tm (M. )Tj 0.0322 Tc 9.5 0 0 9.5 189.5 101.17 Tm (Harada, )Tj 0.05 Tc 9.65 0 0 9.5 224.9 101.17 Tm (On )Tj 0.0446 Tc 9.5 0 0 9.5 240.67 101.17 Tm (binary )Tj 0.0398 Tc 3.096 0 Td (extremal )Tj 0.0039 Tc 4.112 0 Td (formally )Tj -0.0253 Tc 3.786 0 Td (self\255)Tj 0.036 Tc -32.301 -1.214 Td (dual )Tj -0.0095 Tc 2.197 0 Td (even )Tj 0.003 Tc 2.256 0 Td (codes, )Tj /T1_1 1 Tf 0.0223 Tc 9.7 0 0 9.7 108.98 89.64 Tm (Kyusbu )Tj /T1_0 1 Tf -0.0064 Tc 9.8 0 0 9.8 143.22 89.64 Tm (J. )Tj /T1_1 1 Tf 0.008 Tc 9.7 0 0 9.7 153.28 89.64 Tm (Matb. )Tj /T1_0 1 Tf 0.0339 Tc 9.5 0 0 9.5 181.33 89.64 Tm (\(submitted\). )Tj -0.035 Tc 8.1464 0 0 9.5 23.2 70.03 Tm ([3] )Tj 9.0852 0 0 9.5 38.32 70.03 Tm (A. )Tj 0.0121 Tc 9.5 0 0 9.5 50.36 70.03 Tm (Bonnecaze, )Tj -0.035 Tc 9.29 0 0 9.5 98.6 70.03 Tm (P. )Tj -0.0184 Tc 9.5 0 0 9.5 109.09 70.03 Tm (Sole )Tj 0.0419 Tc 1.978 0 Td (and )Tj -0.0021 Tc 1.808 0 Td (A.R. )Tj 0.0282 Tc 2.208 0 Td (Calderbank, )Tj 0.05 Tc 9.5814 0 0 9.5 218.06 70.03 Tm (Quaternary )Tj 0.046 Tc 9.5 0 0 9.5 267.93 70.03 Tm (quadratic )Tj -0.0008 Tc 4.404 0 Td (residue )Tj -0.0048 Tc 3.175 0 Td (codes )Tj 0.0419 Tc -31.738 -1.213 Td (and )Tj 0.0398 Tc 1.924 0 Td (unimodular )Tj 0.0248 Tc 5.316 0 Td (lattices, )Tj /T1_1 1 Tf 0.0231 Tc 9.7 0 0 9.7 142.12 58.51 Tm (IEEE )Tj /T1_0 1 Tf 0.05 Tc 10.585 0 0 9.5 167.75 58.51 Tm (nans. )Tj 0.0097 Tc 9.5 0 0 9.5 195.95 58.51 Tm (Inform. )Tj /T1_1 1 Tf 0.03 Tc 9.7 0 0 9.7 230.02 58.51 Tm (Tbeory )Tj /T1_0 1 Tf 0.05 Tc 9.742 0 0 9.3 262.4 58.51 Tm (41 )Tj -0.035 Tc 10.182 0 0 10.3 277.26 58.51 Tm (\(1995\), )Tj 10.2512 0 0 10.3 308.58 58.51 Tm (366-377. )Tj 9.5671 0 0 10.3 183.54 23.05 Tm (237 )Tj ET endstream endobj 66 0 obj 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