Information on Result #1312350
Linear OA(877, 524, F8, 29) (dual of [524, 447, 30]-code), using 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) based on linear OA(876, 517, F8, 29) (dual of [517, 441, 30]-code), using
- construction XX applied to C1 = C([510,26]), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([510,27]) [i] based on
- 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 = {−1,0,…,26}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(873, 511, F8, 28) (dual of [511, 438, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(876, 511, F8, 29) (dual of [511, 435, 30]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,27}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(870, 511, F8, 27) (dual of [511, 441, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code) (see above)
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(877, 524, F8, 2, 29) (dual of [(524, 2), 971, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(877, 524, F8, 3, 29) (dual of [(524, 3), 1495, 30]-NRT-code) | [i] | ||
| 3 | Digital (48, 77, 524)-net over F8 | [i] | ||