Information on Result #672174
Linear OA(2222, 4194328, F2, 21) (dual of [4194328, 4194106, 22]-code), using construction X4 applied to Ce(20) ⊂ Ce(18) based on
- linear OA(2221, 4194304, F2, 21) (dual of [4194304, 4194083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2199, 4194304, F2, 19) (dual of [4194304, 4194105, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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 OA(2222, 4194328, F2, 20) (dual of [4194328, 4194106, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2223, 4194329, F2, 21) (dual of [4194329, 4194106, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2224, 4194330, F2, 21) (dual of [4194330, 4194106, 22]-code) | [i] | ||
| 4 | Linear OA(2225, 4194331, F2, 21) (dual of [4194331, 4194106, 22]-code) | [i] | ||
| 5 | Linear OA(2226, 4194332, F2, 21) (dual of [4194332, 4194106, 22]-code) | [i] | ||
| 6 | Linear OA(2221, 4194327, F2, 20) (dual of [4194327, 4194106, 21]-code) | [i] | Truncation | |
| 7 | Linear OOA(2222, 2097164, F2, 2, 21) (dual of [(2097164, 2), 4194106, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2222, 1048582, F2, 4, 21) (dual of [(1048582, 4), 4194106, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2222, 524291, F2, 8, 21) (dual of [(524291, 8), 4194106, 22]-NRT-code) | [i] | ||