Information on Result #686027
Linear OA(771, 80, F7, 49) (dual of [80, 9, 50]-code), using construction X applied to C([0,24]) ⊂ C([0,16]) based on
- linear OA(749, 50, F7, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,7)), using the expurgated narrow-sense BCH-code C(I) with length 50 | 74−1, defining interval I = [0,24], and minimum distance d ≥ |{−14,−3,8,…,14}|+1 = 50 (BCH-bound) [i]
- linear OA(741, 50, F7, 33) (dual of [50, 9, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 50 | 74−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(722, 30, F7, 15) (dual of [30, 8, 16]-code), using
- construction X applied to C([1,47]) ⊂ C([1,35]) [i] based on
- linear OA(719, 24, F7, 15) (dual of [24, 5, 16]-code), using contraction [i] based on linear OA(767, 72, F7, 47) (dual of [72, 5, 48]-code), using the narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(716, 24, F7, 11) (dual of [24, 8, 12]-code), using contraction [i] based on linear OA(764, 72, F7, 35) (dual of [72, 8, 36]-code), using the narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(73, 6, F7, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,7) or 6-cap in PG(2,7)), using
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- Reed–Solomon code RS(4,7) [i]
- discarding factors / shortening the dual code based on linear OA(73, 7, F7, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
- construction X applied to C([1,47]) ⊂ C([1,35]) [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.
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(771, 40, F7, 2, 49) (dual of [(40, 2), 9, 50]-NRT-code) | [i] | OOA Folding | |