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A family of 2‐weight codes related to BCH ‐codes
Author(s) -
Bierbrauer Jürgen,
Edel Yves
Publication year - 1997
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1997)5:5<391::aid-jcd7>3.0.co;2-a
Subject(s) - mathematics , combinatorics , prime power , dimension (graph theory) , prime (order theory) , code (set theory) , discrete mathematics , minimum weight , linear code , block code , statistics , computer science , decoding methods , set (abstract data type) , programming language
For every prime‐power q and every pair of natural numbers m ≤ n ′, we construct a q ‐ary linear code of length q m ( q n′ − 1)( q n′ − q n′−m + 1)/( q − 1) and dimension 3 n ′, whose only nonzero weights are $q^{2n'+m-1} - q^{2n'-1}$ and $q^{2n'+m-1} - q^{2n'-1} + q^{n'+m-1}$ . These code parameters and those of the corresponding family of strongly regular graphs are new in odd characteristic. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 391–396, 1997