CASA Function: SakataDecode

Decode using Sakata's algorithm.

Calling Sequence:

• a := SakataDecode(w, C, EL, way)
• a := SakataDecode(w, C, EL)

Parameters:

w : list, vector

• The received word

C : casa/finite/Goppa/primary

• The primary Goppa code (one point with 2 nongaps)

EL : function

• The initialisation of the Sakata algorithm: GoppaPrepareSa(C)

way : string

• Determines whether decoding should be done by finding roots ("root" - the default of an error-locator or determining all syndroms ("syndrom").

Result:

a : vector

• The message sent out.

Description:

• Decodes a received word using Sakata's approach. Where all steps which must be computed once are computed by GoppaPrepareSa
• The vector returned is the most probable message sent out.

Examples:

> infolevel[`casa/finite`] := 5;

> C1 := finiteCurve(x^3 + y^2 + y, finiteField(4));

> H1 := GoppaPrimary(C1, "affine", 4);

> w := [ 1 $ (H1["n"]-1), 0 ];

> Sa := GoppaPrepareSa(H1):

> SakataDecode(w, H1, Sa, "root");

See Also: