Information on Result #674132
Linear OA(293, 144, F2, 30) (dual of [144, 51, 31]-code), using construction XX applied to C([1,28]) ⊂ C([1,26]) ⊂ C([1,22]) based on
- linear OA(284, 127, F2, 30) (dual of [127, 43, 31]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,28], and minimum distance d ≥ 31 (sporadic result) [i]
- linear OA(277, 127, F2, 26) (dual of [127, 50, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(270, 127, F2, 22) (dual of [127, 57, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25, 13, F2, 3) (dual of [13, 8, 4]-code or 13-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(23, 4, F2, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,2) or 4-cap in PG(2,2)), using
- dual of repetition code with length 4 [i]
- caps in base b = 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(294, 145, F2, 31) (dual of [145, 51, 32]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(293, 72, F2, 2, 30) (dual of [(72, 2), 51, 31]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(293, 48, F2, 3, 30) (dual of [(48, 3), 51, 31]-NRT-code) | [i] | ||