Information on Result #674161
Linear OA(249, 67, F2, 23) (dual of [67, 18, 24]-code), using construction X applied to Ce(22) ⊂ Ce(20) based on
- linear OA(248, 64, F2, 23) (dual of [64, 16, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(246, 64, F2, 21) (dual of [64, 18, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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.
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(249, 67, F2, 22) (dual of [67, 18, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(249, 67, F2, 21) (dual of [67, 18, 22]-code) | [i] | ||
| 3 | Linear OA(249, 67, F2, 20) (dual of [67, 18, 21]-code) | [i] | ||
| 4 | Linear OA(250, 68, F2, 23) (dual of [68, 18, 24]-code) | [i] | Code Embedding in Larger Space | |
| 5 | Linear OA(251, 69, F2, 23) (dual of [69, 18, 24]-code) | [i] | ||
| 6 | Linear OA(252, 70, F2, 23) (dual of [70, 18, 24]-code) | [i] | ||
| 7 | Linear OA(253, 71, F2, 23) (dual of [71, 18, 24]-code) | [i] | ||
| 8 | Linear OA(248, 66, F2, 22) (dual of [66, 18, 23]-code) | [i] | Truncation | |
| 9 | Linear OA(247, 65, F2, 21) (dual of [65, 18, 22]-code) | [i] | ||
| 10 | Linear OA(244, 62, F2, 18) (dual of [62, 18, 19]-code) | [i] | ||
| 11 | Linear OA(2260, 322, F2, 86) (dual of [322, 62, 87]-code) | [i] | Construction X with Cyclic Codes | |
| 12 | Linear OA(2259, 322, F2, 86) (dual of [322, 63, 87]-code) | [i] | ||
| 13 | Linear OOA(249, 33, F2, 2, 23) (dual of [(33, 2), 17, 24]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(249, 22, F2, 3, 23) (dual of [(22, 3), 17, 24]-NRT-code) | [i] | ||
| 15 | Linear OOA(249, 13, F2, 5, 23) (dual of [(13, 5), 16, 24]-NRT-code) | [i] | ||