Information on Result #2495068
Linear OOA(4114, 524300, F4, 2, 15) (dual of [(524300, 2), 1048486, 16]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4112, 524299, F4, 2, 15) (dual of [(524299, 2), 1048486, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4112, 1048598, F4, 15) (dual of [1048598, 1048486, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(4111, 1048576, F4, 15) (dual of [1048576, 1048465, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(14) ⊂ Ce(12) [i] based on
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(4115, 524300, F4, 2, 15) (dual of [(524300, 2), 1048485, 16]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(4114, 524300, F4, 3, 15) (dual of [(524300, 3), 1572786, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (99, 114, 524300)-net over F4 | [i] | ||