Information on Result #1288033
Linear OA(2242, 258, F2, 112) (dual of [258, 16, 113]-code), using construction Y1 based on
- linear OA(2243, 264, F2, 112) (dual of [264, 21, 113]-code), using
- 1 times truncation [i] based on linear OA(2244, 265, F2, 113) (dual of [265, 21, 114]-code), using
- construction X applied to Ce(118) ⊂ Ce(110) [i] based on
- linear OA(2243, 256, F2, 119) (dual of [256, 13, 120]-code), using an extension Ce(118) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,118], and designed minimum distance d ≥ |I|+1 = 119 [i]
- linear OA(2235, 256, F2, 111) (dual of [256, 21, 112]-code), using an extension Ce(110) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,110], and designed minimum distance d ≥ |I|+1 = 111 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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(118) ⊂ Ce(110) [i] based on
- 1 times truncation [i] based on linear OA(2244, 265, F2, 113) (dual of [265, 21, 114]-code), using
- nonexistence of OA(221, 264, S2, 6), because
- discarding factors would yield OA(221, 233, S2, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 108418 > 221 [i]
- discarding factors would yield OA(221, 233, S2, 6), but
Mode: 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(2243, 259, F2, 113) (dual of [259, 16, 114]-code) | [i] | Adding a Parity Check Bit | |