Information on Result #2227035
Linear OA(2232, 2097173, F2, 22) (dual of [2097173, 2096941, 23]-code), using 1 times truncation based on linear OA(2233, 2097174, F2, 23) (dual of [2097174, 2096941, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2232, 2097152, F2, 23) (dual of [2097152, 2096920, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2211, 2097152, F2, 21) (dual of [2097152, 2096941, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 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(2232, 1048586, F2, 2, 22) (dual of [(1048586, 2), 2096940, 23]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2232, 699057, F2, 3, 22) (dual of [(699057, 3), 2096939, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(2232, 524293, F2, 4, 22) (dual of [(524293, 4), 2096940, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(2232, 419434, F2, 5, 22) (dual of [(419434, 5), 2096938, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(2232, 349528, F2, 6, 22) (dual of [(349528, 6), 2096936, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(2232, 299596, F2, 7, 22) (dual of [(299596, 7), 2096940, 23]-NRT-code) | [i] | ||
| 7 | Linear OOA(2232, 262146, F2, 8, 22) (dual of [(262146, 8), 2096936, 23]-NRT-code) | [i] | ||
| 8 | Linear OOA(2232, 190652, F2, 22, 22) (dual of [(190652, 22), 4194112, 23]-NRT-code) | [i] | OA Folding and Stacking | |