Information on Result #686262
Linear OA(8109, 2097169, F8, 18) (dual of [2097169, 2097060, 19]-code), using construction X applied to Ce(17) ⊂ Ce(14) 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(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(83, 17, F8, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-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 OOA(8109, 1211420, F8, 2, 18) (dual of [(1211420, 2), 2422731, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8109, 1211420, F8, 3, 18) (dual of [(1211420, 3), 3634151, 19]-NRT-code) | [i] | ||
| 3 | Digital (91, 109, 1211420)-net over F8 | [i] | ||
| 4 | Linear OOA(8109, 1048584, F8, 2, 18) (dual of [(1048584, 2), 2097059, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(8109, 699056, F8, 3, 18) (dual of [(699056, 3), 2097059, 19]-NRT-code) | [i] | ||