Information on Result #2611151
Linear OOA(298, 1369, F2, 3, 16) (dual of [(1369, 3), 4009, 17]-NRT-code), using strength reduction based on linear OOA(298, 1369, F2, 3, 17) (dual of [(1369, 3), 4009, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(298, 4107, F2, 17) (dual of [4107, 4009, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(298, 4109, F2, 17) (dual of [4109, 4011, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(297, 4096, F2, 17) (dual of [4096, 3999, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(298, 4109, F2, 17) (dual of [4109, 4011, 18]-code), 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 | Linear OOA(298, 1261, F2, 4, 16) (dual of [(1261, 4), 4946, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(298, 1261, F2, 5, 16) (dual of [(1261, 5), 6207, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(298, 1261, F2, 6, 16) (dual of [(1261, 6), 7468, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(298, 1261, F2, 7, 16) (dual of [(1261, 7), 8729, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(298, 1261, F2, 8, 16) (dual of [(1261, 8), 9990, 17]-NRT-code) | [i] | ||
| 6 | Digital (82, 98, 1261)-net over F2 | [i] | ||