Information on Result #672454
Linear OA(2172, 131090, F2, 21) (dual of [131090, 130918, 22]-code), using construction X applied to Ce(20) ⊂ Ce(18) based on
- linear OA(2171, 131072, F2, 21) (dual of [131072, 130901, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2154, 131072, F2, 19) (dual of [131072, 130918, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 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(2172, 131090, F2, 20) (dual of [131090, 130918, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2173, 131091, F2, 21) (dual of [131091, 130918, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2174, 131092, F2, 21) (dual of [131092, 130918, 22]-code) | [i] | ||
| 4 | Linear OA(2175, 131093, F2, 21) (dual of [131093, 130918, 22]-code) | [i] | ||
| 5 | Linear OA(2176, 131094, F2, 21) (dual of [131094, 130918, 22]-code) | [i] | ||
| 6 | Linear OA(2171, 131089, F2, 20) (dual of [131089, 130918, 21]-code) | [i] | Truncation | |
| 7 | Linear OOA(2172, 65545, F2, 2, 21) (dual of [(65545, 2), 130918, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2172, 43696, F2, 3, 21) (dual of [(43696, 3), 130916, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2172, 32772, F2, 4, 21) (dual of [(32772, 4), 130916, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2172, 26218, F2, 5, 21) (dual of [(26218, 5), 130918, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(2172, 21848, F2, 6, 21) (dual of [(21848, 6), 130916, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(2172, 18727, F2, 7, 21) (dual of [(18727, 7), 130917, 22]-NRT-code) | [i] | ||
| 13 | Linear OOA(2172, 16386, F2, 8, 21) (dual of [(16386, 8), 130916, 22]-NRT-code) | [i] | ||
| 14 | Linear OOA(2172, 13108, F2, 21, 21) (dual of [(13108, 21), 275096, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |