Information on Result #1535558
Linear OOA(4103, 2097165, F4, 3, 12) (dual of [(2097165, 3), 6291392, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4103, 2097165, F4, 2, 12) (dual of [(2097165, 2), 4194227, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4101, 2097164, F4, 2, 12) (dual of [(2097164, 2), 4194227, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4101, 4194328, F4, 12) (dual of [4194328, 4194227, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(478, 4194304, F4, 10) (dual of [4194304, 4194226, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 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 X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(4101, 4194328, F4, 12) (dual of [4194328, 4194227, 13]-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(4103, 1048582, F4, 15, 12) (dual of [(1048582, 15), 15728627, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |