Information on Result #1589136
Linear OOA(267, 18572, F2, 4, 9) (dual of [(18572, 4), 74221, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(267, 18572, F2, 3, 9) (dual of [(18572, 3), 55649, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(267, 21851, F2, 3, 9) (dual of [(21851, 3), 65486, 10]-NRT-code), using
- 21 times duplication [i] based on linear OOA(266, 21851, F2, 3, 9) (dual of [(21851, 3), 65487, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(266, 65553, F2, 9) (dual of [65553, 65487, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(265, 65536, F2, 9) (dual of [65536, 65471, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(249, 65536, F2, 7) (dual of [65536, 65487, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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 X applied to Ce(8) ⊂ Ce(6) [i] based on
- OOA 3-folding [i] based on linear OA(266, 65553, F2, 9) (dual of [65553, 65487, 10]-code), using
- 21 times duplication [i] based on linear OOA(266, 21851, F2, 3, 9) (dual of [(21851, 3), 65487, 10]-NRT-code), using
Mode: 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(267, 18571, F2, 5, 9) (dual of [(18571, 5), 92788, 10]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(267, 18571, F2, 6, 9) (dual of [(18571, 6), 111359, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(267, 18571, F2, 7, 9) (dual of [(18571, 7), 129930, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(267, 18571, F2, 8, 9) (dual of [(18571, 8), 148501, 10]-NRT-code) | [i] | ||