Information on Result #1539401
Linear OOA(4174, 32782, F4, 3, 29) (dual of [(32782, 3), 98172, 30]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4174, 32782, F4, 2, 29) (dual of [(32782, 2), 65390, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4174, 65564, F4, 29) (dual of [65564, 65390, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-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(4174, 6556, F4, 33, 29) (dual of [(6556, 33), 216174, 30]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |