Information on Result #2220124
Linear OA(245, 4194327, F2, 4) (dual of [4194327, 4194282, 5]-code), using 1 times truncation based on linear OA(246, 4194328, F2, 5) (dual of [4194328, 4194282, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(245, 4194304, F2, 5) (dual of [4194304, 4194259, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(223, 4194304, F2, 3) (dual of [4194304, 4194281, 4]-code or 4194304-cap in PG(22,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 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
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 OOA(245, 4194327, F2, 2, 4) (dual of [(4194327, 2), 8388609, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(245, 4194327, F2, 3, 4) (dual of [(4194327, 3), 12582936, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(245, 2097163, F2, 2, 4) (dual of [(2097163, 2), 4194281, 5]-NRT-code) | [i] | OOA Folding | |