Information on Result #686357
Linear OA(8126, 2097214, F8, 19) (dual of [2097214, 2097088, 20]-code), using construction X applied to Ce(18) ⊂ Ce(10) based on
- linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(813, 62, F8, 7) (dual of [62, 49, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-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(8127, 2097215, F8, 19) (dual of [2097215, 2097088, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8126, 1048607, F8, 2, 19) (dual of [(1048607, 2), 2097088, 20]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8126, 699071, F8, 3, 19) (dual of [(699071, 3), 2097087, 20]-NRT-code) | [i] | ||