Minimal permutation sets for decoding the binary Golay codes (Corresp.)

Partial permutation decoding for binary linear Hadamard codes

“…As a consequence, 3-PD-sets of size m+1 2 + 2 are also found for these codes. Small PD-sets that satisfy the Gordon-Schönheim bound have been found for binary Golay codes [4,10] and for the binary simplex code S 4 [5,6].…”

General Methods of Decoding of Linear Codes

“…This method is called decoding with the help of covering polynomials 1 . Let be the vector (covering polynomial), which coincides with error vector e on the positions of the information set and with zeroes on the other positions.…”

“…Actually finding set G is very difficult. A few nontrivial examples are found in [1], [2], and [3]; see also [4]. Therefore, to implement the general information-set decoding algorithm, we have to specify a way of choosing information sets.…”

Partial permutation decoding for codes from affine geometry designs

“…Such sets might not exist at all, and the property of having a PD-set will not, in general, be invariant under isomorphism of codes, i.e. it depends on the choice of I and C. Furthermore, there is a bound on the minimum size of S (see [5], [13], or [6]). This bound can be adapted to one for s-PD-sets by replacing in the formula for the bound, the variable t, that denotes full error-correction, by s < t for correction of s errors.…”

“…τ to the points (0, 0, 0), (2,11,5), (3,10,7). For the first coordinate triple [0, 2, 3], the map δ (10) takes this to the standard form [0, 1,11] and the map δ(2)τ (13) takes this to the triple [13,15,16].…”