Information on Result #686139
Linear OA(763, 76, F7, 40) (dual of [76, 13, 41]-code), using construction XX applied to Ce(39) ⊂ Ce(31) ⊂ Ce(25) based on
- linear OA(745, 49, F7, 40) (dual of [49, 4, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(740, 49, F7, 32) (dual of [49, 9, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(736, 49, F7, 26) (dual of [49, 13, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(710, 19, F7, 8) (dual of [19, 9, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using
- extended Reed–Solomon code RSe(4,7) [i]
- algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [i]
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(763, 38, F7, 2, 40) (dual of [(38, 2), 13, 41]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(763, 25, F7, 3, 40) (dual of [(25, 3), 12, 41]-NRT-code) | [i] | ||