Information on Result #1535705
Linear OOA(4107, 8171, F4, 3, 21) (dual of [(8171, 3), 24406, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4107, 8171, F4, 2, 21) (dual of [(8171, 2), 16235, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4107, 8196, F4, 2, 21) (dual of [(8196, 2), 16285, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4107, 16392, F4, 21) (dual of [16392, 16285, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(41, 8, F4, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- OOA 2-folding [i] based on linear OA(4107, 16392, F4, 21) (dual of [16392, 16285, 22]-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(4107, 2042, F4, 27, 21) (dual of [(2042, 27), 55027, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |