Information on Result #1288017
Linear OA(283, 175, F2, 22) (dual of [175, 92, 23]-code), using construction Y1 based on
- linear OA(284, 255, F2, 22) (dual of [255, 171, 23]-code), using
- the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- nonexistence of linear OA(2171, 255, F2, 80) (dual of [255, 84, 81]-code), because
- discarding factors / shortening the dual code would yield linear OA(2171, 235, F2, 80) (dual of [235, 64, 81]-code), but
- construction Y1 [i] would yield
- linear OA(2170, 211, F2, 80) (dual of [211, 41, 81]-code), but
- construction Y1 [i] would yield
- linear OA(2169, 197, F2, 80) (dual of [197, 28, 81]-code), but
- adding a parity check bit [i] would yield linear OA(2170, 198, F2, 81) (dual of [198, 28, 82]-code), but
- OA(241, 211, S2, 14), but
- discarding factors would yield OA(241, 198, S2, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 206433 399776 > 241 [i]
- discarding factors would yield OA(241, 198, S2, 14), but
- linear OA(2169, 197, F2, 80) (dual of [197, 28, 81]-code), but
- construction Y1 [i] would yield
- OA(264, 235, S2, 24), but
- discarding factors would yield OA(264, 218, S2, 24), but
- the Rao or (dual) Hamming bound shows that M ≥ 18 753208 478511 637348 > 264 [i]
- discarding factors would yield OA(264, 218, S2, 24), but
- linear OA(2170, 211, F2, 80) (dual of [211, 41, 81]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(2171, 235, F2, 80) (dual of [235, 64, 81]-code), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.