Information on Result #673949
Linear OA(2170, 178, F2, 87) (dual of [178, 8, 88]-code), using construction X applied to Ce(126) ⊂ Ce(62) based on
- linear OA(2127, 128, F2, 127) (dual of [128, 1, 128]-code or 128-arc in PG(126,2)), using an extension Ce(126) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,126], and designed minimum distance d ≥ |I|+1 = 127 [i]
- linear OA(2120, 128, F2, 63) (dual of [128, 8, 64]-code), using an extension Ce(62) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(243, 50, F2, 23) (dual of [50, 7, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(243, 51, F2, 23) (dual of [51, 8, 24]-code), using
- concatenation of two codes [i] based on
- discarding factors / shortening the dual code based on linear OA(243, 51, F2, 23) (dual of [51, 8, 24]-code), using
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(2169, 177, F2, 86) (dual of [177, 8, 87]-code) | [i] | Truncation | |
| 2 | Linear OOA(2170, 89, F2, 2, 87) (dual of [(89, 2), 8, 88]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2170, 59, F2, 3, 87) (dual of [(59, 3), 7, 88]-NRT-code) | [i] | ||