Bounds on the state complexity of codes from the Hermitian function field and its subfields

نویسندگان

  • Yaron Shany
  • Yair Be'ery
چکیده

An upper bound on the minimal state complexity of codes from the Hermitian function field and some of its subfields is derived. Coordinate orderings under which the state complexity of the codes is not above the bound are specified. For the self-dual Hermitian code it is proved that the bound coincides with the minimal state complexity of the code. Finally, it is shown that Hermitian codes over fields of characteristic 2 admit a recursive twisted squaring construction.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

. N T ] 2 3 Ju l 2 01 7 ON SUBFIELDS OF THE HERMITIAN FUNCTION FIELDS INVOLVING THE INVOLUTION AUTOMORPHISM

A function field over a finite field is called maximal if it achieves the Hasse-Weil bound. Finding possible genera that maximal function fields achieve has both theoretical interest and practical applications to coding theory and other topics. As a subfield of a maximal function field is also maximal, one way to find maximal function fields is to find all subfields of a maximal function field....

متن کامل

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

متن کامل

Riemann-roch Spaces of the Hermitian Function Field with Applications to Algebraic Geometry Codes and Low-discrepancy Sequences

This paper is concerned with two applications of bases of Riemann-Roch spaces. In the first application, we define the floor of a divisor and obtain improved bounds on the parameters of algebraic geometry codes. These bounds apply to a larger class of codes than that of Homma and Kim (Goppa codes with Weierstrass pairs, J. Pure Appl. Algebra 162 (2001), 273-290). Then we determine explicit base...

متن کامل

Construction of Global Function Fields from Linear Codes and vice Versa

We introduce a new connection between linear codes and global function fields, which in turn allows us to construct new global function fields with improved lower bounds on the number of rational places. The genus and number of rational places of subfields of certain families of cyclotomic function fields are given as well.

متن کامل

An Overview of the Civil Liability of the Modern State (Concept, Resources, Foundations)

Modern state is conceptually and subjectively complicated as per the wide range of concepts and subjects related to it, therefore the context is provided to present the viewpoints on its identity and nature. Based on this, human sciences Scientifics investigate it from different perspectives. Complexity of the nature of modern State, arises the various theories around it, despite bring serious ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • IEEE Trans. Information Theory

دوره 46  شماره 

صفحات  -

تاریخ انتشار 2000