Information on Result #672846
Linear OA(2110, 4109, F2, 19) (dual of [4109, 3999, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(297, 4096, F2, 17) (dual of [4096, 3999, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(2110, 4109, F2, 18) (dual of [4109, 3999, 19]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2111, 4110, F2, 19) (dual of [4110, 3999, 20]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2112, 4111, F2, 19) (dual of [4111, 3999, 20]-code) | [i] | ||
| 4 | Linear OA(2113, 4112, F2, 19) (dual of [4112, 3999, 20]-code) | [i] | ||
| 5 | Linear OA(2114, 4113, F2, 19) (dual of [4113, 3999, 20]-code) | [i] | ||
| 6 | Linear OA(2109, 4108, F2, 18) (dual of [4108, 3999, 19]-code) | [i] | Truncation | |
| 7 | Linear OOA(2110, 2054, F2, 2, 19) (dual of [(2054, 2), 3998, 20]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2110, 1369, F2, 3, 19) (dual of [(1369, 3), 3997, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(2110, 1027, F2, 4, 19) (dual of [(1027, 4), 3998, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(2110, 821, F2, 5, 19) (dual of [(821, 5), 3995, 20]-NRT-code) | [i] | ||
| 11 | Linear OOA(2110, 684, F2, 6, 19) (dual of [(684, 6), 3994, 20]-NRT-code) | [i] | ||
| 12 | Linear OOA(2110, 587, F2, 7, 19) (dual of [(587, 7), 3999, 20]-NRT-code) | [i] | ||
| 13 | Linear OOA(2110, 513, F2, 8, 19) (dual of [(513, 8), 3994, 20]-NRT-code) | [i] | ||
| 14 | Linear OOA(2110, 456, F2, 19, 19) (dual of [(456, 19), 8554, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |