Information on Result #823314
Linear OOA(4105, 32785, F4, 2, 17) (dual of [(32785, 2), 65465, 18]-NRT-code), using OOA 2-folding based on linear OA(4105, 65570, F4, 17) (dual of [65570, 65465, 18]-code), using
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(10) [i] based on
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(465, 65536, F4, 11) (dual of [65536, 65471, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(45, 31, F4, 3) (dual of [31, 26, 4]-code or 31-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), 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(4105, 32785, F4, 3, 17) (dual of [(32785, 3), 98250, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (88, 105, 32785)-net over F4 | [i] | ||