BINARY CODES
        BINARY CODES DATABASES
             MAGMAPackages
                    by
              Jaume Pujol and Merc`e Villanueva
          Combinatorics, Coding and Security Group (CCSG)
             Autonomous University of Barcelona
                  Barcelona
                  April 7, 2015
           2
                  Contents
                  1 Binary Codes                                                                   7
                      1.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .    7
                      1.2  Construction of Binary Codes . . . . . . . . . . . . . . . . . .        9
                      1.3  Invariants of a Binary Code . . . . . . . . . . . . . . . . . . .      13
                      1.4  The Information Sets . . . . . . . . . . . . . . . . . . . . . . .     15
                      1.5  Operations on Codewords . . . . . . . . . . . . . . . . . . . .        16
                      1.6  Membership and Equality . . . . . . . . . . . . . . . . . . . .        16
                      1.7  Properties of Binary Codes . . . . . . . . . . . . . . . . . . . .     17
                      1.8  The Weight and Distance Distribution . . . . . . . . . . . . .         19
                      1.9  Union, Intersection and Dual . . . . . . . . . . . . . . . . . . .     25
                      1.10 New Codes from Existing        . . . . . . . . . . . . . . . . . . . . 26
                      1.11 Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   28
                  2 Binary Codes Database                                                        31
                      2.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .   31
                      2.2  Databases of binary (extended) 1-perfect codes . . . . . . . . .       31
                  Bibliography                                                                   39
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           4                          CONTENTS