Patterson Decoder for binary Goppa codes

[giucesare]

Decoder for binary Goppa codes whose defining polynomials are square free which uses Patterson decoding algorithm in order to correct errors in words.
The Patterson decoder makes use of the terminated extended Euclidean algorithm.
For further details see

N. Patterson: The algebraic decoding of Goppa codes, IEEE Transactions on Information Theory 21.2 (1975), pp. 203-207.

Johan S. H. Rosenkilde gave us a feedback on the first draft of this decoder and also suggested us possible reviewers.
So, we would like to thank him.

CC: @xcaruso @dimpase

Component: coding theory

Keywords: coding theory, goppa codes, patterson decoder

Author: Giuseppe Cesare, Ferdinando Zullo

Branch/Commit: u/gh-giucesare/patterson_decoder @ e62cd8a

Reviewer: Xavier Caruso, Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/31723

[giucesare]

Attachment: patterson_decoder.py.gz

Patterson Decoder

[dimpase]

comment:1

Could you post a branch, rather than an attachment?

[giucesare]

Description changed:

--- 
+++ 
@@ -2,8 +2,7 @@
 The Patterson decoder makes use of the terminated extended Euclidean algorithm.
 For further details see 
 
-N. Patterson: The algebraic decoding of Goppa codes, IEEE Transactions on
-Information Theory 21.2 (1975), pp. 203-207.
+N. Patterson: The algebraic decoding of Goppa codes, IEEE Transactions on Information Theory 21.2 (1975), pp. 203-207.
 
 Johan S. H. Rosenkilde gave us a feedback on the first draft of this decoder and also suggested us possible reviewers. 
 So, we would like to thank him.

[giucesare]

Branch: u/gh-giucesare/31723-patterson_decoder_for_binary_goppa_codes

[giucesare]

Changed branch from u/gh-giucesare/31723-patterson_decoder_for_binary_goppa_codes to none

[giucesare]

Branch: u/gh-giucesare/31723-patterson_decoder_for_binary_goppa_codes

[giucesare]

Changed branch from u/gh-giucesare/31723-patterson_decoder_for_binary_goppa_codes to none

[giucesare]

Branch: u/gh-giucesare/31723-patterson_decoder_for_binary_goppa_codes

[giucesare]

Changed branch from u/gh-giucesare/31723-patterson_decoder_for_binary_goppa_codes to none

[giucesare]

Branch: u/gh-giucesare/patterson_decoder

[giucesare]

comment:10

after many attempts maybe I did it correctly now... sorry, this is my first ticket.

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New commits:

e62cd8a

Decoder for binary Goppa codes whose defining polynomials are square free which uses Patterson decoding algorithm in order to correct errors in words.