Information on Result #687512
Linear OA(871, 4107, F8, 20) (dual of [4107, 4036, 21]-code), using construction XX applied to Ce(19) ⊂ Ce(17) ⊂ Ce(16) based on
- linear OA(869, 4096, F8, 20) (dual of [4096, 4027, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(861, 4096, F8, 18) (dual of [4096, 4035, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(857, 4096, F8, 17) (dual of [4096, 4039, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(81, 10, F8, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(871, 3497, F8, 2, 20) (dual of [(3497, 2), 6923, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(871, 3497, F8, 3, 20) (dual of [(3497, 3), 10420, 21]-NRT-code) | [i] | ||
| 3 | Digital (51, 71, 3497)-net over F8 | [i] | ||
| 4 | Linear OOA(871, 2053, F8, 2, 20) (dual of [(2053, 2), 4035, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(871, 1369, F8, 3, 20) (dual of [(1369, 3), 4036, 21]-NRT-code) | [i] | ||