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Extended Irreducible Binary Sextic Goppa Codes.
- Source :
- IEEE Transactions on Information Theory; Jan2022, Vol. 68 Issue 1, p230-237, 8p
- Publication Year :
- 2022
-
Abstract
- Let $n (>3)$ be a prime number and ${\mathbb {F}}_{2^{n}}$ a finite field of $2^{n}$ elements. Let $L ={\mathbb {F}}_{2^{n}}\cup \{\infty \}$ be the support set and $g(x)$ an irreducible polynomial of degree 6 over ${\mathbb {F}}_{2^{n}}$. In this paper, we obtain an upper bound on the number of extended irreducible binary Goppa codes $\Gamma (L, g)$ of degree 6 and length $2^{n}+1$. [ABSTRACT FROM AUTHOR]
- Subjects :
- BINARY codes
PRIME numbers
FINITE fields
REED-Solomon codes
IRREDUCIBLE polynomials
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 154265871
- Full Text :
- https://doi.org/10.1109/TIT.2021.3116659