Information on Result #686278
Linear OA(851, 2097168, F8, 8) (dual of [2097168, 2097117, 9]-code), using construction X4 applied to Ce(8) ⊂ Ce(5) based on
- 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(836, 2097152, F8, 6) (dual of [2097152, 2097116, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(815, 16, F8, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,8)), using
- dual of repetition code with length 16 [i]
- linear OA(81, 16, F8, 1) (dual of [16, 15, 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
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(852, 2097169, F8, 8) (dual of [2097169, 2097117, 9]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(851, 2097168, F8, 2, 8) (dual of [(2097168, 2), 4194285, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(851, 2097168, F8, 3, 8) (dual of [(2097168, 3), 6291453, 9]-NRT-code) | [i] | ||
| 4 | Digital (43, 51, 2097168)-net over F8 | [i] | ||
| 5 | Linear OOA(851, 1048584, F8, 2, 8) (dual of [(1048584, 2), 2097117, 9]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(851, 699056, F8, 3, 8) (dual of [(699056, 3), 2097117, 9]-NRT-code) | [i] | ||
| 7 | Linear OOA(851, 524292, F8, 8, 8) (dual of [(524292, 8), 4194285, 9]-NRT-code) | [i] | OA Folding and Stacking | |