Information on Result #686300
Linear OA(874, 2097176, F8, 12) (dual of [2097176, 2097102, 13]-code), using construction X applied to Ce(11) ⊂ Ce(8) based on
- linear OA(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
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 OA(875, 2097177, F8, 12) (dual of [2097177, 2097102, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(874, 2097176, F8, 2, 12) (dual of [(2097176, 2), 4194278, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(874, 2097176, F8, 3, 12) (dual of [(2097176, 3), 6291454, 13]-NRT-code) | [i] | ||
| 4 | Digital (62, 74, 2097176)-net over F8 | [i] | ||
| 5 | Linear OA(875, 2097178, F8, 12) (dual of [2097178, 2097103, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(876, 2097180, F8, 12) (dual of [2097180, 2097104, 13]-code) | [i] | ||
| 7 | Linear OOA(874, 1048588, F8, 2, 12) (dual of [(1048588, 2), 2097102, 13]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(874, 699058, F8, 3, 12) (dual of [(699058, 3), 2097100, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(874, 349529, F8, 12, 12) (dual of [(349529, 12), 4194274, 13]-NRT-code) | [i] | OA Folding and Stacking | |