Information on Result #699763
Linear OA(12855, 2097167, F128, 18) (dual of [2097167, 2097112, 19]-code), using construction X applied to Ce(17) ⊂ Ce(13) based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1283, 15, F128, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), 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 | OA(3277, 2097167, S32, 18) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6465, 2097167, S64, 18) | [i] | ||
| 3 | Linear OOA(12855, 1048583, F128, 2, 18) (dual of [(1048583, 2), 2097111, 19]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(12855, 699055, F128, 3, 18) (dual of [(699055, 3), 2097110, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(12855, 524291, F128, 4, 18) (dual of [(524291, 4), 2097109, 19]-NRT-code) | [i] | ||