Information on Result #1312096
Linear OA(842, 682, F8, 14) (dual of [682, 640, 15]-code), using 160 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 20 times 0, 1, 49 times 0, 1, 82 times 0) based on linear OA(837, 517, F8, 14) (dual of [517, 480, 15]-code), using
- construction XX applied to C1 = C([510,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([510,12]) [i] based on
- linear OA(834, 511, F8, 13) (dual of [511, 477, 14]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(834, 511, F8, 13) (dual of [511, 477, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(837, 511, F8, 14) (dual of [511, 474, 15]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(831, 511, F8, 12) (dual of [511, 480, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [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(842, 682, F8, 2, 14) (dual of [(682, 2), 1322, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(842, 682, F8, 3, 14) (dual of [(682, 3), 2004, 15]-NRT-code) | [i] | ||
| 3 | Digital (28, 42, 682)-net over F8 | [i] | ||