Information on Result #685638
Linear OA(769, 183, F7, 28) (dual of [183, 114, 29]-code), using construction X applied to Ce(28) ⊂ Ce(22) based on
- linear OA(764, 172, F7, 29) (dual of [172, 108, 30]-code), using an extension Ce(28) of the narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(758, 172, F7, 23) (dual of [172, 114, 24]-code), using an extension Ce(22) of the narrow-sense BCH-code C(I) with length 171 | 73−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(75, 11, F7, 4) (dual of [11, 6, 5]-code), using
- construction X applied to AG(F, Q+0P) ⊂ AG(F, Q+1P) [i] based on
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using 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]
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8 (see above)
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F, Q+0P) ⊂ AG(F, Q+1P) [i] based on
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(769, 91, F7, 2, 28) (dual of [(91, 2), 113, 29]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(769, 61, F7, 3, 28) (dual of [(61, 3), 114, 29]-NRT-code) | [i] | ||