Information on Result #679060
Linear OA(430, 16393, F4, 6) (dual of [16393, 16363, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(4) based on
- linear OA(429, 16384, F4, 6) (dual of [16384, 16355, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(422, 16384, F4, 5) (dual of [16384, 16362, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
- dual of repetition code with length 9 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 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 OA(431, 16394, F4, 6) (dual of [16394, 16363, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(430, 16393, F4, 2, 6) (dual of [(16393, 2), 32756, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(430, 16393, F4, 3, 6) (dual of [(16393, 3), 49149, 7]-NRT-code) | [i] | ||
| 4 | Digital (24, 30, 16393)-net over F4 | [i] | ||
| 5 | Linear OOA(430, 8196, F4, 2, 6) (dual of [(8196, 2), 16362, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(430, 5464, F4, 3, 6) (dual of [(5464, 3), 16362, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(430, 5464, F4, 6, 6) (dual of [(5464, 6), 32754, 7]-NRT-code) | [i] | OA Folding and Stacking | |