Information on Result #734497
Linear OA(4955, 2508, F49, 20) (dual of [2508, 2453, 21]-code), using (u, u+v)-construction based on
- linear OA(4916, 105, F49, 10) (dual of [105, 89, 11]-code), using
- construction XX applied to C1 = C([21,29]), C2 = C([20,27]), C3 = C1 + C2 = C([21,27]), and C∩ = C1 ∩ C2 = C([20,29]) [i] based on
- linear OA(4913, 100, F49, 9) (dual of [100, 87, 10]-code), using the BCH-code C(I) with length 100 | 492−1, defining interval I = {21,22,…,29}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4913, 100, F49, 8) (dual of [100, 87, 9]-code), using the BCH-code C(I) with length 100 | 492−1, defining interval I = {20,21,…,27}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(4915, 100, F49, 10) (dual of [100, 85, 11]-code), using the BCH-code C(I) with length 100 | 492−1, defining interval I = {20,21,…,29}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(4911, 100, F49, 7) (dual of [100, 89, 8]-code), using the BCH-code C(I) with length 100 | 492−1, defining interval I = {21,22,…,27}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(491, 3, F49, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- Reed–Solomon code RS(48,49) [i]
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([21,29]), C2 = C([20,27]), C3 = C1 + C2 = C([21,27]), and C∩ = C1 ∩ C2 = C([20,29]) [i] based on
- linear OA(4939, 2403, F49, 20) (dual of [2403, 2364, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(4939, 2401, F49, 20) (dual of [2401, 2362, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(4937, 2401, F49, 19) (dual of [2401, 2364, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code) (see above)
- construction X applied to Ce(19) ⊂ Ce(18) [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(4955, 1254, F49, 2, 20) (dual of [(1254, 2), 2453, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4955, 836, F49, 3, 20) (dual of [(836, 3), 2453, 21]-NRT-code) | [i] | ||