Information on Result #712472
Linear OA(751, 70, F7, 30) (dual of [70, 19, 31]-code), using construction XX applied to C1 = C([41,17]), C2 = C([0,23]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([41,23]) based on
- linear OA(735, 48, F7, 25) (dual of [48, 13, 26]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,17}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,23}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(727, 48, F7, 18) (dual of [48, 21, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(78, 14, F7, 6) (dual of [14, 6, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(78, 19, F7, 6) (dual of [19, 11, 7]-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 OA(750, 69, F7, 29) (dual of [69, 19, 30]-code) | [i] | Truncation | |
| 2 | Linear OOA(751, 35, F7, 2, 30) (dual of [(35, 2), 19, 31]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(751, 23, F7, 3, 30) (dual of [(23, 3), 18, 31]-NRT-code) | [i] | ||