Information on Result #712515
Linear OA(756, 67, F7, 38) (dual of [67, 11, 39]-code), using construction XX applied to C1 = C([41,25]), C2 = C([0,31]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([41,31]) based on
- linear OA(742, 48, F7, 33) (dual of [48, 6, 34]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,25}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(744, 48, F7, 39) (dual of [48, 4, 40]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,31}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(736, 48, F7, 26) (dual of [48, 12, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(76, 11, F7, 5) (dual of [11, 5, 6]-code), using
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(77, 8, F7, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using code C1 for u = 2 by de Boer and Brouwer [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using code C0 for u = 2 by de Boer and Brouwer [i]
- 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 C1 ⊂ C0 [i] based on
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)) (see above)
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(756, 33, F7, 2, 38) (dual of [(33, 2), 10, 39]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(756, 22, F7, 3, 38) (dual of [(22, 3), 10, 39]-NRT-code) | [i] | ||