Information on Result #1420423
Linear OOA(464, 1048602, F4, 2, 8) (dual of [(1048602, 2), 2097140, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(464, 1048602, F4, 8) (dual of [1048602, 1048538, 9]-code), using
- construction X with Varšamov bound [i] 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
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(462, 1048600, F4, 7) (dual of [1048600, 1048538, 8]-code), using Gilbert–Varšamov bound and bm = 462 > Vbs−1(k−1) = 1 346003 790727 972992 545653 683674 636377 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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
- linear OA(462, 1048598, F4, 8) (dual of [1048598, 1048536, 9]-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(464, 524301, F4, 3, 8) (dual of [(524301, 3), 1572839, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(464, 524300, F4, 10, 8) (dual of [(524300, 10), 5242936, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |