Information on Result #678870
Linear OA(495, 65567, F4, 15) (dual of [65567, 65472, 16]-code), using construction XX applied to Ce(14) ⊂ Ce(10) ⊂ Ce(9) 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(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(457, 65536, F4, 10) (dual of [65536, 65479, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-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(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(495, 42613, F4, 2, 15) (dual of [(42613, 2), 85131, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(495, 42613, F4, 3, 15) (dual of [(42613, 3), 127744, 16]-NRT-code) | [i] | ||
| 3 | Digital (80, 95, 42613)-net over F4 | [i] | ||
| 4 | Linear OOA(495, 32783, F4, 2, 15) (dual of [(32783, 2), 65471, 16]-NRT-code) | [i] | OOA Folding | |