Information on Result #699776
Linear OA(12856, 2097171, F128, 18) (dual of [2097171, 2097115, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) 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(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), 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(3279, 2097171, S32, 18) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6466, 2097171, S64, 18) | [i] | ||
| 3 | Linear OOA(12856, 1048585, F128, 2, 18) (dual of [(1048585, 2), 2097114, 19]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(12856, 699057, F128, 3, 18) (dual of [(699057, 3), 2097115, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(12856, 524292, F128, 4, 18) (dual of [(524292, 4), 2097112, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(12856, 233019, F128, 18, 18) (dual of [(233019, 18), 4194286, 19]-NRT-code) | [i] | OA Folding and Stacking | |