Moved and fixed list of decoder types

src/doc/en/thematic_tutorials/coding_theory.rst

@@ -417,20 +417,6 @@ follows::
     sage: D.decoder_type()
     {'always-succeed', 'complete', 'hard-decision', 'unique'}
 
-One can find the list of all decoder type with their definition here:
-
-- **always-succeed**: always returns the original codeword,
-- **complete**: can decode every word in the ambient space of the code,
-- **half-minimum-distance**: cannot decode if there are more errors than half
-  the minimum dustance of the code,
-- **hard-decision**: returns a codeword computed with an algorithm which
-  is not probabilistic,
-- **list-decoder**: returns a list of codewords which contains the original
-- **might-fail**: might return a codeword which is not the original codeword,
-  codeword,
-- **unique**: returns a single codeword.
-
-
 IV. A deeper look at channels
 =============================
 

src/sage/coding/decoder.py

@@ -140,8 +140,34 @@ def decoder_type(self):
         Returns the set of types of ``self``. These types describe the nature of ``self``
         and its decoding algorithm.
 
-        One can find a complete description of the types in the
-        introductory thematic tutorial on coding theory.
+        A complete description of types follows:
+
+        +-----------------------+--------------------------------------------+
+        | Decoder Type          | Description                                |
+        +=======================+============================================+
+        | always-succeed        | Always return the original codeword if     |
+        |                       | the number of errors is up to the decoding |
+        |                       | radius                                     |
+        +-----------------------+--------------------------------------------+
+        | complete              | Can decode every word in the ambient space |
+        |                       | of the code                                |
+        +-----------------------+--------------------------------------------+
+        | half-minimum-distance | Its decoding radius is at most half the    |
+        |                       | minimum distance of the code               |
+        +-----------------------+--------------------------------------------+
+        | hard-decision         | The symbols of the input word are          |
+        |                       | taken from a finite set of values          |
+        |                       | without any clue on their reliability      |
+        +-----------------------+--------------------------------------------+
+        | list-decoder          | Returns a list of codewords                |
+        +-----------------------+--------------------------------------------+
+        | might-fail            | Might fail at returning anything at all    |
+        +-----------------------+--------------------------------------------+
+        | might-error           | Might return a codeword which is not the   |
+        |                       | original codeword                          |
+        +-----------------------+--------------------------------------------+
+        | unique                | Returns a single codeword                  |
+        +-----------------------+--------------------------------------------+
 
         EXAMPLES::