Information on Result #686345
Linear OA(8117, 2097205, F8, 18) (dual of [2097205, 2097088, 19]-code), using construction X applied to Ce(17) ⊂ Ce(10) 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(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(811, 53, F8, 6) (dual of [53, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-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(8118, 2097206, F8, 18) (dual of [2097206, 2097088, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8118, 2097207, F8, 18) (dual of [2097207, 2097089, 19]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(8117, 1048602, F8, 2, 18) (dual of [(1048602, 2), 2097087, 19]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(8117, 699068, F8, 3, 18) (dual of [(699068, 3), 2097087, 19]-NRT-code) | [i] | ||