Index Abelian group , 13 5 absolute trac e function , 1 5 adjoining elements , 6 , 14 4 Advanced Encryptio n Standar d (AES), 11 2 efficiency, 11 9 affine geometry , 66 , 78 , 16 0 affine plane , 60 , 7 7 affine space , 5 9 algebraic extension , 8 , 9 annihilates, 2 3 Artin's lemma , 23 , 14 1 Assmus, E . F. , Jr. , 10 4 automorphism, 14 , 29 , 14 1 balanced incomplet e bloc k design , 67 basis complementary, 2 2 dual, 22 , 14 9 finite field, 1 9 normal, 20 , 2 3 polynomial, 1 9 primitive normal , 2 5 self-dual normal , 25 , 4 0 vector space , 14 8 BCH code , 9 7 designed distance , 9 7 Betti-Mathieu group , 4 1 BIBD, see balance d incomplet e block desig n Bose, Ra j Chandra , 4 7 Cayley table , 44 , 77 , 15 9 character o f a group , 7 2 quadratic, 7 3 characteristic (ring) , 2 , 13 8 characteristic polynomial , 16 , 2 3 Chinese remainde r theorem , 15 0 ciphertext, 11 0 closed binar y operation , 13 5 code, 80 , see also error-correctin g code BCH, see BC H cod e const ant-weight, 10 2 cyclic, 9 5 decoding methods , 9 1 dual, 10 1 equivalent, 9 6 Golay, see Gola y cod e Goppa, 9 8 Hamming, see Hammin g cod e linear, 8 2 narrow-sense, 9 7 parity-check, 8 2 perfect, 89 , 10 2 primitive, 9 7 rate, 8 7 Reed-Solomon, 9 7 171
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