Information on Result #1312332
Linear OA(875, 531, F8, 28) (dual of [531, 456, 29]-code), using 9 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0) based on linear OA(874, 521, F8, 28) (dual of [521, 447, 29]-code), using
- construction XX applied to C1 = C([509,24]), C2 = C([0,25]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C([509,25]) [i] based on
- linear OA(870, 511, F8, 27) (dual of [511, 441, 28]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(867, 511, F8, 26) (dual of [511, 444, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(873, 511, F8, 28) (dual of [511, 438, 29]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,25}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(864, 511, F8, 25) (dual of [511, 447, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(81, 7, F8, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(875, 531, F8, 2, 28) (dual of [(531, 2), 987, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(875, 531, F8, 3, 28) (dual of [(531, 3), 1518, 29]-NRT-code) | [i] | ||
| 3 | Digital (47, 75, 531)-net over F8 | [i] | ||