Information on Result #2239722
Linear OA(479, 65567, F4, 12) (dual of [65567, 65488, 13]-code), using 1 times truncation based on linear OA(480, 65568, F4, 13) (dual of [65568, 65488, 14]-code), using
- construction XX applied to Ce(12) ⊂ Ce(8) ⊂ Ce(6) [i] based on
- 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(449, 65536, F4, 9) (dual of [65536, 65487, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(441, 65536, F4, 7) (dual of [65536, 65495, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(479, 65567, F4, 2, 12) (dual of [(65567, 2), 131055, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(479, 65567, F4, 3, 12) (dual of [(65567, 3), 196622, 13]-NRT-code) | [i] | ||
| 3 | Digital (67, 79, 65567)-net over F4 | [i] | ||