Information on Result #672520
Linear OA(2178, 65553, F2, 23) (dual of [65553, 65375, 24]-code), using construction X applied to Ce(22) ⊂ Ce(20) based on
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2161, 65536, F2, 21) (dual of [65536, 65375, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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(2178, 65553, F2, 22) (dual of [65553, 65375, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2179, 65554, F2, 23) (dual of [65554, 65375, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2180, 65555, F2, 23) (dual of [65555, 65375, 24]-code) | [i] | ||
| 4 | Linear OA(2181, 65556, F2, 23) (dual of [65556, 65375, 24]-code) | [i] | ||
| 5 | Linear OA(2182, 65557, F2, 23) (dual of [65557, 65375, 24]-code) | [i] | ||
| 6 | Linear OA(2177, 65552, F2, 22) (dual of [65552, 65375, 23]-code) | [i] | Truncation | |
| 7 | Linear OOA(2178, 32776, F2, 2, 23) (dual of [(32776, 2), 65374, 24]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2178, 21851, F2, 3, 23) (dual of [(21851, 3), 65375, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2178, 16388, F2, 4, 23) (dual of [(16388, 4), 65374, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2178, 13110, F2, 5, 23) (dual of [(13110, 5), 65372, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(2178, 10925, F2, 6, 23) (dual of [(10925, 6), 65372, 24]-NRT-code) | [i] | ||
| 12 | Linear OOA(2178, 9364, F2, 7, 23) (dual of [(9364, 7), 65370, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(2178, 8194, F2, 8, 23) (dual of [(8194, 8), 65374, 24]-NRT-code) | [i] | ||
| 14 | Linear OOA(2178, 5959, F2, 23, 23) (dual of [(5959, 23), 136879, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |