Information on Result #1698279
Linear OOA(2133, 16389, F2, 8, 16) (dual of [(16389, 8), 130979, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2133, 16389, F2, 4, 16) (dual of [(16389, 4), 65423, 17]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2132, 16389, F2, 4, 16) (dual of [(16389, 4), 65424, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2132, 65556, F2, 16) (dual of [65556, 65424, 17]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2129, 65553, F2, 16) (dual of [65553, 65424, 17]-code), using
- 1 times truncation [i] based on linear OA(2130, 65554, F2, 17) (dual of [65554, 65424, 18]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2129, 65536, F2, 17) (dual of [65536, 65407, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
- dual of repetition code with length 18 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 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
- 1 times truncation [i] based on linear OA(2130, 65554, F2, 17) (dual of [65554, 65424, 18]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2129, 65553, F2, 16) (dual of [65553, 65424, 17]-code), using
- OOA 4-folding [i] based on linear OA(2132, 65556, F2, 16) (dual of [65556, 65424, 17]-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(2133, 16388, F2, 24, 16) (dual of [(16388, 24), 393179, 17]-NRT-code) | [i] | OOA Stacking with Additional Row | |