Information on Result #1312022
Linear OA(818, 698, F8, 6) (dual of [698, 680, 7]-code), using 179 step Varšamov–Edel lengthening with (ri) = (1, 33 times 0, 1, 144 times 0) based on linear OA(816, 517, F8, 6) (dual of [517, 501, 7]-code), using
- construction XX applied to C1 = C([510,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([510,4]) [i] based on
- linear OA(813, 511, F8, 5) (dual of [511, 498, 6]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(813, 511, F8, 5) (dual of [511, 498, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(816, 511, F8, 6) (dual of [511, 495, 7]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(810, 511, F8, 4) (dual of [511, 501, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [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(818, 698, F8, 2, 6) (dual of [(698, 2), 1378, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(818, 698, F8, 3, 6) (dual of [(698, 3), 2076, 7]-NRT-code) | [i] | ||
| 3 | Digital (12, 18, 698)-net over F8 | [i] | ||
| 4 | Linear OOA(818, 349, F8, 2, 6) (dual of [(349, 2), 680, 7]-NRT-code) | [i] | OOA Folding | |