Information on Result #2417382
Linear OOA(271, 131, F2, 2, 18) (dual of [(131, 2), 191, 19]-NRT-code), using strength reduction based on linear OOA(271, 131, F2, 2, 19) (dual of [(131, 2), 191, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(271, 262, F2, 19) (dual of [262, 191, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(270, 261, F2, 19) (dual of [261, 191, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(269, 256, F2, 19) (dual of [256, 187, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(265, 256, F2, 17) (dual of [256, 191, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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(18) ⊂ Ce(16) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(270, 261, F2, 19) (dual of [261, 191, 20]-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(271, 131, F2, 3, 18) (dual of [(131, 3), 322, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(271, 131, F2, 4, 18) (dual of [(131, 4), 453, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(271, 131, F2, 5, 18) (dual of [(131, 5), 584, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(271, 131, F2, 6, 18) (dual of [(131, 6), 715, 19]-NRT-code) | [i] | ||
| 5 | Linear OOA(271, 131, F2, 7, 18) (dual of [(131, 7), 846, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(271, 131, F2, 8, 18) (dual of [(131, 8), 977, 19]-NRT-code) | [i] | ||
| 7 | Digital (53, 71, 131)-net over F2 | [i] | ||