Affine Variety Codes over a Hyperelliptic Curve

2021 ◽  
Vol 57 (1) ◽  
pp. 84-97
Author(s):  
N. Patanker ◽  
S. K. Singh
Keyword(s):  
Hyperelliptic Curve ◽  
Affine Variety ◽  
Affine Variety Codes

scholarly journals On affine variety codes from the Klein quartic

2018 ◽  
Vol 11 (2) ◽  
pp. 237-257 ◽  
Author(s):  
Olav Geil ◽  
Ferruh Özbudak
Keyword(s):  
Affine Variety ◽  
Affine Variety Codes

scholarly journals Improved decoding of affine-variety codes

2012 ◽  
Vol 216 (7) ◽  
pp. 1533-1565 ◽  
Author(s):  
Chiara Marcolla ◽  
Emmanuela Orsini ◽  
Massimiliano Sala
Keyword(s):  
Affine Variety ◽  
Affine Variety Codes

scholarly journals On the distance of stabilizer quantum codes from J-affine variety codes

2017 ◽  
Vol 16 (4) ◽  
Author(s):  
Carlos Galindo ◽  
Olav Geil ◽  
Fernando Hernando ◽  
Diego Ruano
Keyword(s):  
Quantum Codes ◽  
Affine Variety ◽  
Affine Variety Codes

scholarly journals Quantum codes from affine variety codes and their subfield-subcodes

2014 ◽  
Vol 76 (1) ◽  
pp. 89-100 ◽  
Author(s):  
Carlos Galindo ◽  
Fernando Hernando
Keyword(s):  
Quantum Codes ◽  
Affine Variety ◽  
Affine Variety Codes

scholarly journals Stabilizer quantum codes from J-affine variety codes and a new Steane-like enlargement

2015 ◽  
Vol 14 (9) ◽  
pp. 3211-3231 ◽  
Author(s):  
Carlos Galindo ◽  
Fernando Hernando ◽  
Diego Ruano
Keyword(s):  
Quantum Codes ◽  
Affine Variety ◽  
Affine Variety Codes

scholarly journals The group of units on an affine variety

2014 ◽  
Vol 13 (08) ◽  
pp. 1450065 ◽  
Author(s):  
Timothy J. Ford
Keyword(s):  
Hyperelliptic Curve ◽  
Sufficient Conditions ◽  
Galois Cohomology ◽  
Closed Field ◽  
Affine Variety ◽  
Cyclic Cover ◽  
Group Of Units ◽  
Object Of Study ◽  
General Affine ◽  
Projective Completion

The object of study is the group of units 𝒪*(X) in the coordinate ring of a normal affine variety X over an algebraically closed field k. Methods of Galois cohomology are applied to those varieties that can be presented as a finite cyclic cover of a rational variety. On a cyclic cover X → 𝔸m of affine m-space over k such that the ramification divisor is irreducible and the degree is prime, it is shown that 𝒪*(X) is equal to k*, the non-zero scalars. The same conclusion holds, if X is a sufficiently general affine hyperelliptic curve. If X has a projective completion such that the divisor at infinity has r components, then sufficient conditions are given for 𝒪*(X)/k* to be isomorphic to ℤ(r-1).

scholarly journals Locally recoverable J-affine variety codes

2020 ◽  
Vol 64 ◽  
pp. 101661 ◽  
Author(s):  
Carlos Galindo ◽  
Fernando Hernando ◽  
Carlos Munuera
Keyword(s):  
Affine Variety ◽  
Affine Variety Codes
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