Results 151 to 160 of about 2,356,486 (173)

A Graphic Characterization of Hermitian Curves

1983
Publisher Summary This chapter presents a graphic characterization of hermitian curves. In PG(2,q), q square, a set ∪ of points is called a Hermitian arc (or a unital) if it is a (q + 1, + 1). In particular, ∪ is called a Hermitian curve if there is a Hermitian polarity for which ∪ is the set of self-conjugate points.
FAINA, Giorgio, G. Korchmaros
openaire   +2 more sources

Fractional decoding of codes from Hermitian curves

2021 IEEE International Symposium on Information Theory (ISIT), 2021
We present a new probabilistic decoding algorithm that can be used to perform fractional decoding of codes from the Hermitian curve. Fractional decoding means that the original codeword may be obtained from a received word using only an $\alpha$ -proportion of symbols of the received word, provided not too many errors have occurred.
Gretchen L. Matthews, Aidan W. Murphy, Welington Santos   +2 more
openaire   +1 more source

Characterization of hermitian curves

Archiv der Mathematik, 1982
info:eu-repo/semantics ...
openaire   +3 more sources

On Certain Subcovers of the Hermitian Curve

Communications in Algebra, 2006
ABSTRACT We present a simple construction that gives explicit equations for certain subcovers of the Hermitian curve. We show that maximal curves with a certain type of defining equations are covered by the Hermitian curve.
Arnaldo Garcia, Motoko Q. Kawakita, Shinji Miura   +2 more
openaire   +1 more source

Codes on hermitian curves

2006
Keywords: algoweb_agcodes Reference ALGO-CONF-1988-001 URL: http://www.springerlink.com/content/g507468741773528/url.pdf Record created on 2007-01-26, modified on 2017-05 ...
openaire   +1 more source

Generalising a characterisation of Hermitian curves

Journal of Geometry, 2001
The authors prove a characterisation of the classical unital that is a generalisation of a characterisation proved in 1982 by Lefevre-Peresy. It is shown that if \({\mathcal U}\) is a Buekenhout-Metz unital with respect to a line \(\ell_\infty\) in \(\text{PG}(2,q^2)\) such that a line of \(\text{PG}(2,q^2)\) not through \({\mathcal U}\cap \ell_\infty\)
Barwick, S., Quinn, C.
openaire   +3 more sources

On the dual minimum distance and minimum weight of codes from a quotient of the Hermitian curve

Applicable Algebra in Engineering, Communication and Computing, 2012
In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form $$y^q+y=x^m,\,q$$yq+y=xm,q being a prime power and $$m$$m a positive integer which divides $$q+1$$q+1.
E. Ballico, A. Ravagnani
semanticscholar   +1 more source

Pointwise Slant Curves in Pseudo-Hermitian Geometry

Mediterranean Journal of Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Vector Bundles and Codes on the Hermitian Curve

IEEE Transactions on Information Theory, 2005
The construction of algebraic-geometry (AG) codes can be seen as a distinctly geometric process, and yet decoding procedures tend to rely on algebraic ideas that have no direct geometric interpretation. Recently, however, Trygve Johnsen observed that decoding can be viewed in abstract terms of a class of vector bundles on the underlying curve.
openaire   +1 more source

Remarks on codes from Hermitian curves

IEEE Trans. Inf. Theory, 1987
Let \(q=r^ 2\), where r is a power of 2. The hermitean curve H in PG(2,q) is given by \(X^{r+1}+Y^{r+1}+Z^{r+1}=0\). It is well known that H has genus r(r-1)/2 and has \(r^ 3+1\) points over \({\mathbb{F}}_ q\). The author takes \(Q=(0,1,1)\) and considers te codes \(C_ m=\{f(r_ 1),f(R_ 2),...,f(R_{p^ 3})|\) \(f\in L(mQ)\}\) as defined in Goppa's ...
openaire   +2 more sources