Designs, Codes and Cryptography

, Volume 45, Issue 2, pp 213–217 | Cite as

A search algorithm for linear codes: progressive dimension growth

  • Tsvetan Asamov
  • Nuh AydinEmail author


This paper presents an algorithm, called progressive dimension growth (PDG), for the construction of linear codes with a pre-specified length and a minimum distance. A number of new linear codes over GF(5) that have been discovered via this algorithm are also presented.


New codes Minimum distance bounds Search algorithm Progressive dimension Growth (PDG) 

AMS Classification



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  1. Aydin N, Siap I and Ray-Chaudhuri DK (2001). The structure of 1-generator quasi-twisted codes and new linear codes. Des Codes Cryptogr 24(3): 313–326 zbMATHCrossRefMathSciNetGoogle Scholar
  2. (2006). Discovering mathematics with magma: reducing the abstract to concrete. Springer, Berlin zbMATHGoogle Scholar
  3. Brouwer AE. Bounds (Bounds on the minimum distance of linear codes). Scholar
  4. Chen EZ (2007). New quasi-cyclic codes from simpex codes. IEEE Trans Inform Theory 53(1): 1193 CrossRefMathSciNetGoogle Scholar
  5. Daskalov R, Gulliver TA and Metodieva E (1999). New ternary linear codes. IEEE Trans Inform Theory 45(5): 1687–1688 zbMATHCrossRefMathSciNetGoogle Scholar
  6. Daskalov R and Hristov P (2003). New quasi-twisted degenerate ternary linear codes. IEEE Trans Inform Theory 49(9): 2259–2263 CrossRefMathSciNetGoogle Scholar
  7. Grassl M. Bounds on the minimum distance of linear codes. http://www.codetables.deGoogle Scholar
  8. Grassl M, White G (2005) New codes from chains of quasi-cyclic codes. In: Proceedings of IEEE international symposium on information theory (ISIT 2005), Adelaide, Australia, September 2005, pp 2095–2099Google Scholar
  9. Gulliver TA and Östergard PRJ (2000). New binary linear codes. Ars Combinatoria 56: 105–112 zbMATHMathSciNetGoogle Scholar
  10. MacWilliams FJ and Sloane NJA (1977). The theory of error correcting codes. North Holland, Amsterdam zbMATHGoogle Scholar
  11. MAGMA computer algebra system. Scholar
  12. Siap I, Aydin N and Ray-Chaudhuri DK (2000). New ternary quasi-cyclic codes with better minimum distances. IEEE Trans Inform Theory 46(4): 1554–1558 zbMATHCrossRefMathSciNetGoogle Scholar
  13. Tsfasman MA and Vlǎdut SG (1991). Algebraic geometry codes. Kluwert, Dordrecht Google Scholar
  14. Vardy A (1997). The intractability of computing the minimum distance of a code. IEEE Trans Inform Theory 43(6): 1757–1766 zbMATHCrossRefMathSciNetGoogle Scholar
  15. White G (preprint) An improved minimum weight algorithm for quasi-cyclic and quasi-twisted codesGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsKenyon CollegeGambierUSA

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