Information on Result #1312030
Linear OA(821, 651, F8, 7) (dual of [651, 630, 8]-code), using 132 step Varšamov–Edel lengthening with (ri) = (1, 24 times 0, 1, 106 times 0) based on linear OA(819, 517, F8, 7) (dual of [517, 498, 8]-code), using
- construction XX applied to C1 = C([510,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([510,5]) [i] based on
- 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(816, 511, F8, 6) (dual of [511, 495, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(819, 511, F8, 7) (dual of [511, 492, 8]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [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(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(821, 651, F8, 2, 7) (dual of [(651, 2), 1281, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(821, 651, F8, 3, 7) (dual of [(651, 3), 1932, 8]-NRT-code) | [i] | ||
| 3 | Digital (14, 21, 651)-net over F8 | [i] | ||
| 4 | Linear OOA(821, 325, F8, 2, 7) (dual of [(325, 2), 629, 8]-NRT-code) | [i] | OOA Folding | |