Information on Result #1312065
Linear OA(836, 1159, F8, 11) (dual of [1159, 1123, 12]-code), using 634 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 13 times 0, 1, 34 times 0, 1, 74 times 0, 1, 122 times 0, 1, 168 times 0, 1, 213 times 0) based on linear OA(828, 517, F8, 11) (dual of [517, 489, 12]-code), using
- construction XX applied to C1 = C([510,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([510,9]) [i] based on
- linear OA(825, 511, F8, 10) (dual of [511, 486, 11]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(825, 511, F8, 10) (dual of [511, 486, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(828, 511, F8, 11) (dual of [511, 483, 12]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(822, 511, F8, 9) (dual of [511, 489, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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(836, 1159, F8, 2, 11) (dual of [(1159, 2), 2282, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(836, 1159, F8, 3, 11) (dual of [(1159, 3), 3441, 12]-NRT-code) | [i] | ||
| 3 | Digital (25, 36, 1159)-net over F8 | [i] | ||