Information on Result #715413
Linear OA(860, 525, F8, 22) (dual of [525, 465, 23]-code), using construction XX applied to C1 = C([509,17]), C2 = C([0,19]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([509,19]) based on
- 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 = {−2,−1,…,17}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(852, 511, F8, 20) (dual of [511, 459, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(858, 511, F8, 22) (dual of [511, 453, 23]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,19}, and designed minimum distance d ≥ |I|+1 = 23 [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(81, 7, F8, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- linear OA(81, 7, F8, 1) (dual of [7, 6, 2]-code) (see above)
Mode: Constructive and 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(860, 525, F8, 2, 22) (dual of [(525, 2), 990, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(860, 525, F8, 3, 22) (dual of [(525, 3), 1515, 23]-NRT-code) | [i] | ||
| 3 | Digital (38, 60, 525)-net over F8 | [i] | ||
| 4 | Linear OOA(860, 262, F8, 2, 22) (dual of [(262, 2), 464, 23]-NRT-code) | [i] | OOA Folding | |