Information on Result #686272
Linear OA(872, 2097168, F8, 12) (dual of [2097168, 2097096, 13]-code), using construction X4 applied to Ce(11) ⊂ Ce(9) 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(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(873, 2097169, F8, 12) (dual of [2097169, 2097096, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(872, 1048584, F8, 2, 12) (dual of [(1048584, 2), 2097096, 13]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(872, 699056, F8, 3, 12) (dual of [(699056, 3), 2097096, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(872, 349528, F8, 12, 12) (dual of [(349528, 12), 4194264, 13]-NRT-code) | [i] | OA Folding and Stacking | |