Information on Result #713526
Linear OA(753, 352, F7, 20) (dual of [352, 299, 21]-code), using construction XX applied to C1 = C([340,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([340,17]) based on
- linear OA(749, 342, F7, 19) (dual of [342, 293, 20]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(746, 342, F7, 18) (dual of [342, 296, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(752, 342, F7, 20) (dual of [342, 290, 21]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,17}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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 OA(754, 360, F7, 20) (dual of [360, 306, 21]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(755, 383, F7, 20) (dual of [383, 328, 21]-code) | [i] | ||
| 3 | Linear OOA(753, 176, F7, 2, 20) (dual of [(176, 2), 299, 21]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(753, 117, F7, 3, 20) (dual of [(117, 3), 298, 21]-NRT-code) | [i] | ||