Information on Result #686358
Linear OA(8119, 2097214, F8, 18) (dual of [2097214, 2097095, 19]-code), using construction X applied to Ce(17) ⊂ Ce(9) based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(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(8120, 2097215, F8, 18) (dual of [2097215, 2097095, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8119, 1048607, F8, 2, 18) (dual of [(1048607, 2), 2097095, 19]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(8119, 699071, F8, 3, 18) (dual of [(699071, 3), 2097094, 19]-NRT-code) | [i] | ||