Information on Result #1590787
Linear OOA(2123, 1208, F2, 4, 20) (dual of [(1208, 4), 4709, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2123, 1208, F2, 3, 20) (dual of [(1208, 3), 3501, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2123, 1370, F2, 3, 20) (dual of [(1370, 3), 3987, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2123, 4110, F2, 20) (dual of [4110, 3987, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2121, 4108, F2, 20) (dual of [4108, 3987, 21]-code), using
- 1 times truncation [i] based on linear OA(2122, 4109, F2, 21) (dual of [4109, 3987, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2121, 4096, F2, 21) (dual of [4096, 3975, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(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
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2122, 4109, F2, 21) (dual of [4109, 3987, 22]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2121, 4108, F2, 20) (dual of [4108, 3987, 21]-code), using
- OOA 3-folding [i] based on linear OA(2123, 4110, F2, 20) (dual of [4110, 3987, 21]-code), using
Mode: 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 OOA(2123, 604, F2, 7, 20) (dual of [(604, 7), 4105, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2123, 604, F2, 8, 20) (dual of [(604, 8), 4709, 21]-NRT-code) | [i] | ||