New bounds on the distance distribution of extended Goppa codes

DOI10.1006/ffta.2001.0340zbMath1016.94043OpenAlexW2018635435MaRDI QIDQ700157

Sarit Zur, Simon N. Litsyn

Publication date: 30 September 2002

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.2001.0340

zbMATH Keywords

exponential sumsGoppa codesKrawtchouk polynomialsdistance distribution

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Bounds on codes (94B65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27)

Cites Work

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• Weight distributions of subfield subcodes of algebraic-geometrical codes
• Exponential Sums and Goppa Codes: I
• Goppa codes
• The weights of the orthogonals of the extended quadratic binary Goppa codes
• The true dimension of certain binary Goppa codes
• A transform approach to Goppa codes
• On the parameters of Goppa codes
• Exponential sums and Goppa codes. II
• On the derivation of Goppa codes (Corresp.)
• Further results on Goppa codes and their applications to constructing efficient binary codes
• Bounds on Goppa codes (Corresp.)
• Equivalent irreducible Goppa codes (Corresp.)
• Bounds on the decoding error probability of binary linear codes via their spectra
• Parameters of Goppa codes revisited
• Extended double-error-correcting binary Goppa codes are cyclic (Corresp.)
• More on the distance distribution of BCH codes
• On spectra of BCH codes
• Subclass of binary Goppa codes with minimal distance equal to the design distance

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