Information on Result #1312191
Linear OA(858, 659, F8, 20) (dual of [659, 601, 21]-code), using 136 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 8 times 0, 1, 21 times 0, 1, 41 times 0, 1, 59 times 0) based on linear OA(852, 517, F8, 20) (dual of [517, 465, 21]-code), using
- construction XX applied to C1 = C([510,17]), C2 = C([0,18]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([510,18]) [i] based on
- linear OA(849, 511, F8, 19) (dual of [511, 462, 20]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(849, 511, F8, 19) (dual of [511, 462, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(852, 511, F8, 20) (dual of [511, 459, 21]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(846, 511, F8, 18) (dual of [511, 465, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [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(858, 659, F8, 2, 20) (dual of [(659, 2), 1260, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(858, 659, F8, 3, 20) (dual of [(659, 3), 1919, 21]-NRT-code) | [i] | ||
| 3 | Digital (38, 58, 659)-net over F8 | [i] | ||