Information on Result #678869
Linear OA(493, 65558, F4, 15) (dual of [65558, 65465, 16]-code), using construction XX applied to Ce(14) ⊂ Ce(12) ⊂ Ce(10) based on
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(41, 19, F4, 1) (dual of [19, 18, 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
- 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(493, 34427, F4, 2, 15) (dual of [(34427, 2), 68761, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(493, 34427, F4, 3, 15) (dual of [(34427, 3), 103188, 16]-NRT-code) | [i] | ||
| 3 | Digital (78, 93, 34427)-net over F4 | [i] | ||
| 4 | Linear OOA(493, 32779, F4, 2, 15) (dual of [(32779, 2), 65465, 16]-NRT-code) | [i] | OOA Folding | |