Information on Result #677922
Linear OA(435, 4194317, F4, 5) (dual of [4194317, 4194282, 6]-code), using construction X4 applied to Ce(4) ⊂ Ce(2) based on
- linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(423, 4194304, F4, 3) (dual of [4194304, 4194281, 4]-code or 4194304-cap in PG(22,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(412, 13, F4, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,4)), using
- dual of repetition code with length 13 [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 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(436, 4194318, F4, 5) (dual of [4194318, 4194282, 6]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(436, 4194319, F4, 5) (dual of [4194319, 4194283, 6]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(435, 2097158, F4, 3, 5) (dual of [(2097158, 3), 6291439, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 4 | Linear OOA(435, 2097158, F4, 5, 5) (dual of [(2097158, 5), 10485755, 6]-NRT-code) | [i] | ||