Information on Result #1165321
Linear OOA(2157, 65539, F2, 8, 17) (dual of [(65539, 8), 524155, 18]-NRT-code), using OOA 8-folding based on linear OA(2157, 524312, F2, 17) (dual of [524312, 524155, 18]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2154, 524309, F2, 17) (dual of [524309, 524155, 18]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2153, 524288, F2, 17) (dual of [524288, 524135, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
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(2158, 65539, F2, 8, 17) (dual of [(65539, 8), 524154, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2156, 65538, F2, 8, 16) (dual of [(65538, 8), 524148, 17]-NRT-code) | [i] | Truncation for OOAs | |