Information on Result #1051958
Linear OOA(298, 1027, F2, 4, 17) (dual of [(1027, 4), 4010, 18]-NRT-code), using OOA 4-folding based on linear OA(298, 4108, F2, 17) (dual of [4108, 4010, 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
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, 1027, F2, 4, 16) (dual of [(1027, 4), 4010, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(299, 1027, F2, 4, 17) (dual of [(1027, 4), 4009, 18]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2100, 1027, F2, 4, 17) (dual of [(1027, 4), 4008, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(298, 1027, F2, 5, 17) (dual of [(1027, 5), 5037, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(298, 1027, F2, 6, 17) (dual of [(1027, 6), 6064, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(298, 1027, F2, 7, 17) (dual of [(1027, 7), 7091, 18]-NRT-code) | [i] | ||
| 7 | Linear OOA(298, 1027, F2, 8, 17) (dual of [(1027, 8), 8118, 18]-NRT-code) | [i] | ||
| 8 | Digital (81, 98, 1027)-net over F2 | [i] | ||