Information on Result #672393
Linear OA(2182, 262163, F2, 21) (dual of [262163, 261981, 22]-code), using construction X applied to Ce(20) ⊂ Ce(18) based on
- linear OA(2181, 262144, F2, 21) (dual of [262144, 261963, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2163, 262144, F2, 19) (dual of [262144, 261981, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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(2182, 262163, F2, 20) (dual of [262163, 261981, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2183, 262164, F2, 21) (dual of [262164, 261981, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2184, 262165, F2, 21) (dual of [262165, 261981, 22]-code) | [i] | ||
| 4 | Linear OA(2185, 262166, F2, 21) (dual of [262166, 261981, 22]-code) | [i] | ||
| 5 | Linear OA(2186, 262167, F2, 21) (dual of [262167, 261981, 22]-code) | [i] | ||
| 6 | Linear OA(2181, 262162, F2, 20) (dual of [262162, 261981, 21]-code) | [i] | Truncation | |
| 7 | Linear OOA(2182, 131081, F2, 2, 21) (dual of [(131081, 2), 261980, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2182, 87387, F2, 3, 21) (dual of [(87387, 3), 261979, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2182, 65540, F2, 4, 21) (dual of [(65540, 4), 261978, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2182, 52432, F2, 5, 21) (dual of [(52432, 5), 261978, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(2182, 43693, F2, 6, 21) (dual of [(43693, 6), 261976, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(2182, 37451, F2, 7, 21) (dual of [(37451, 7), 261975, 22]-NRT-code) | [i] | ||
| 13 | Linear OOA(2182, 32770, F2, 8, 21) (dual of [(32770, 8), 261978, 22]-NRT-code) | [i] | ||
| 14 | Linear OOA(2182, 26216, F2, 21, 21) (dual of [(26216, 21), 550354, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |