Information on Result #673896
Linear OA(272, 264, F2, 19) (dual of [264, 192, 20]-code), using construction XX applied to Ce(18) ⊂ Ce(16) ⊂ Ce(14) 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 OA(271, 263, F2, 18) (dual of [263, 192, 19]-code) | [i] | Truncation | |
| 2 | Linear OOA(272, 132, F2, 2, 19) (dual of [(132, 2), 192, 20]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(272, 88, F2, 3, 19) (dual of [(88, 3), 192, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(272, 66, F2, 4, 19) (dual of [(66, 4), 192, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(272, 44, F2, 6, 19) (dual of [(44, 6), 192, 20]-NRT-code) | [i] | ||