Information on Result #822899
Linear OOA(492, 524299, F4, 2, 12) (dual of [(524299, 2), 1048506, 13]-NRT-code), using OOA 2-folding based on linear OA(492, 1048598, F4, 12) (dual of [1048598, 1048506, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(471, 1048576, F4, 10) (dual of [1048576, 1048505, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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: Constructive and 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(494, 524300, F4, 2, 12) (dual of [(524300, 2), 1048506, 13]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(493, 524299, F4, 2, 12) (dual of [(524299, 2), 1048505, 13]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(492, 524299, F4, 3, 12) (dual of [(524299, 3), 1572805, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (80, 92, 524299)-net over F4 | [i] | ||