The complete weight enumerator of Type II codes over Z/sub 2m/ and Jacobi forms

2001 ◽  
Vol 47 (1) ◽  
pp. 396-399 ◽  
Author(s):  
Young Ju Choie ◽  
Namshik Kim
Keyword(s):  
Weight Enumerator ◽  
Type Ii ◽  
Jacobi Forms ◽  
Complete Weight Enumerator ◽  
Type Ii Codes

Byte weight enumerators and modular forms of genus r

2015 ◽  
Vol 14 (06) ◽  
pp. 1550080
Author(s):  
Anuradha Sharma ◽  
Amit K. Sharma
Keyword(s):  
Modular Forms ◽  
Quadratic Forms ◽  
Zeta Functions ◽  
Siegel Modular Forms ◽  
Type I ◽  
Type Ii ◽  
Jacobi Forms ◽  
Weight Enumerators ◽  
Type Ii Codes ◽  
Real Quaternions

For a positive integer m, let R be either the ring ℤ2m of integers modulo 2m or the quaternionic ring Σ2m = ℤ2m + αℤ2m + βℤ2m + γℤ2m with α = 1 + î, β = 1 + ĵ and [Formula: see text], where [Formula: see text] are elements of the ring ℍ of real quaternions satisfying [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. In this paper, we obtain Jacobi forms (or Siegel modular forms) of genus r from byte weight enumerators (or symmetrized byte weight enumerators) in genus r of Type I and Type II codes over R. Furthermore, we derive a functional equation for partial Epstein zeta functions, which are summands of classical Epstein zeta functions associated with quadratic forms.

Self-dual codes over the ring GR(pm,g) and Jacobi forms

2017 ◽  
Vol 10 (03) ◽  
pp. 1750055 ◽  
Author(s):  
Ankur
Keyword(s):  
Polynomial Ring ◽  
Galois Ring ◽  
The Self ◽  
Weight Enumerator ◽  
Invariant Polynomial ◽  
Jacobi Forms ◽  
Dual Codes ◽  
Complete Weight Enumerator ◽  
Weil Group ◽  
The Relationship

We take a Galois ring [Formula: see text] and discuss about the self-dual codes and its properties over the ring. We will also describe the relationship between Clifford-Weil group and Jacobi forms by constructing the invariant polynomial ring with the complete weight enumerator.

Type II Codes over IF2r

2001 ◽  
pp. 102-111 ◽  
Author(s):  
Koichi Betsumiya ◽  
Masaaki Harada ◽  
Akihiro Munemasa
Keyword(s):  
Type Ii ◽  
Type Ii Codes

Type II codes over Z/sub 4/

1997 ◽  
Vol 43 (3) ◽  
pp. 969-976 ◽  
Author(s):  
A. Bonnecaze ◽  
P. Sole ◽  
C. Bachoc ◽  
B. Mourrain
Keyword(s):  
Type Ii ◽  
Type Ii Codes

scholarly journals EISENSTEIN POLYNOMIALS ASSOCIATED TO BINARY CODES

2009 ◽  
Vol 05 (04) ◽  
pp. 635-640 ◽  
Author(s):  
MANABU OURA
Keyword(s):  
Binary Codes ◽  
Weighted Sum ◽  
Type Ii ◽  
Weight Enumerators ◽  
Fixed Length ◽  
Type Ii Codes ◽  
Genus 2

The Eisenstein polynomial is the weighted sum of the weight enumerators of all classes of Type II codes of fixed length. In this note, we investigate the ring generated by Eisenstein polynomials in genus 2.

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