Information on Result #1535949
Linear OOA(4113, 8195, F4, 3, 22) (dual of [(8195, 3), 24472, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4113, 8195, F4, 2, 22) (dual of [(8195, 2), 16277, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4113, 16390, F4, 22) (dual of [16390, 16277, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4113, 16391, F4, 22) (dual of [16391, 16278, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4113, 16391, F4, 22) (dual of [16391, 16278, 23]-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(4113, 2048, F4, 27, 22) (dual of [(2048, 27), 55183, 23]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |