Information on Result #678708
Linear OA(4130, 65562, F4, 20) (dual of [65562, 65432, 21]-code), using construction X4 applied to Ce(21) ⊂ Ce(17) based on
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(425, 26, F4, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,4)), using
- dual of repetition code with length 26 [i]
- linear OA(41, 26, F4, 1) (dual of [26, 25, 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 OOA(4130, 51958, F4, 2, 20) (dual of [(51958, 2), 103786, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4130, 51958, F4, 3, 20) (dual of [(51958, 3), 155744, 21]-NRT-code) | [i] | ||
| 3 | Digital (110, 130, 51958)-net over F4 | [i] | ||