Information on Result #806301
Linear OOA(272, 132, F2, 2, 19) (dual of [(132, 2), 192, 20]-NRT-code), using OOA 2-folding based on linear OA(272, 264, F2, 19) (dual of [264, 192, 20]-code), using
- construction XX applied to Ce(18) ⊂ Ce(16) ⊂ Ce(14) [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(257, 256, F2, 15) (dual of [256, 199, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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
- linear OA(21, 2, F2, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- Reed–Solomon code RS(1,2) [i]
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(272, 120, F2, 3, 19) (dual of [(120, 3), 288, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(272, 120, F2, 4, 19) (dual of [(120, 4), 408, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(272, 120, F2, 5, 19) (dual of [(120, 5), 528, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(272, 120, F2, 6, 19) (dual of [(120, 6), 648, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(272, 120, F2, 7, 19) (dual of [(120, 7), 768, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(272, 120, F2, 8, 19) (dual of [(120, 8), 888, 20]-NRT-code) | [i] | ||
| 7 | Digital (53, 72, 120)-net over F2 | [i] | ||