Information on Result #1420384
Linear OOA(462, 1048598, F4, 2, 8) (dual of [(1048598, 2), 2097134, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(462, 1048598, F4, 8) (dual of [1048598, 1048536, 9]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(461, 1048576, F4, 9) (dual of [1048576, 1048515, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(441, 1048576, F4, 6) (dual of [1048576, 1048535, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(421, 22, F4, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,4)), using
- dual of repetition code with length 22 [i]
- linear OA(41, 22, F4, 1) (dual of [22, 21, 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
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(462, 524299, F4, 3, 8) (dual of [(524299, 3), 1572835, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(462, 524298, F4, 10, 8) (dual of [(524298, 10), 5242918, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |