Skip to main content
SpringerLink
Log in

The Complete Determination of the Minimum Distance of Two-Point Codes on a Hermitian Curve

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

This is a continuation of the previous papers [3, 4, 5]. We finish determining the minimum distance of two-point codes on a Hermitian curve.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M Homma (1996) ArticleTitleThe Weierstrass semigroup of a pair of points on a curve Arch Math 67 337–348 Occurrence Handle0869.14015 Occurrence Handle97j:14034 Occurrence Handle10.1007/BF01197599

    Article  MATH  MathSciNet  Google Scholar 

  2. M Homma S J Kim (2001) ArticleTitleGoppa codes with Weierstrass pairs J Pure Appl Algebra 162 273–290 Occurrence Handle2002d:14047 Occurrence Handle10.1016/S0022-4049(00)00134-1

    Article  MathSciNet  Google Scholar 

  3. M Homma S J Kim (2005) ArticleTitleToward the determination of the minimum distance of two-point codes on a Hermitian curve Des Codes Cryptogr 37 111–132 Occurrence Handle2165044 Occurrence Handle10.1007/s10623-004-3807-5

    Article  MathSciNet  Google Scholar 

  4. M Homma S J Kim (2006) ArticleTitleThe two-point codes on a Hermitian curve with the designed minimum distance Des Codes Cryptogr 38 55–81 Occurrence Handle2191125 Occurrence Handle10.1007/s10623-004-5661-x

    Article  MathSciNet  Google Scholar 

  5. M Homma S J Kim (2006) ArticleTitleThe two-point codes with the designed distance on a Hermitian curve in even characteristic Des Codes Cryptogr 39 375–386 Occurrence Handle2191125 Occurrence Handle10.1007/s10623-005-5471-9

    Article  MathSciNet  Google Scholar 

  6. S J Kim (1994) ArticleTitleOn the index of the Weierstrass semigroup of a pair of points on a curve Arch Math 62 73–82 Occurrence Handle0815.14020 Occurrence Handle10.1007/BF01200442

    Article  MATH  Google Scholar 

  7. G L Matthews (2001) ArticleTitleWeierstrass pairs and minimum distance of Goppa codes Designs Codes Cryptogr 22 107–121 Occurrence Handle0989.94032 Occurrence Handle2002a:14024 Occurrence Handle10.1023/A:1008311518095

    Article  MATH  MathSciNet  Google Scholar 

  8. Yang K, Kumar P V (1992). On the true minimum distance of Hermitian codes. In: (Stichtenoth H, Tsfasman M A (eds) Coding theory and algebraic geometry, Lecture note in mathematics, Berlin-Heidelberg 1518, pp 99–107. Springer-Verlag

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kanagawa University, Yokohama, 221–8686, Japan

    Masaaki Homma

  2. Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660–701, Korea

    Seon Jeong Kim

Authors
  1. Masaaki Homma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seon Jeong Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seon Jeong Kim.

Additional information

Communicated by J.D. Key

Masaaki Homma: Partially supported by Grant-in-Aid for Scientific Research (15500017), JSPS.

Seon Jeong Kim: Partially supported by Korea Research Foundation Grant (KRF-2004-041-C00016)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Homma, M., Kim, S.J. The Complete Determination of the Minimum Distance of Two-Point Codes on a Hermitian Curve. Des Codes Crypt 40, 5–24 (2006). https://doi.org/10.1007/s10623-005-4599-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-005-4599-y

Keywords

AMS Classification

Search

Navigation