Information on Result #677935
Linear OA(4189, 4194328, F4, 23) (dual of [4194328, 4194139, 24]-code), using construction X4 applied to Ce(22) ⊂ Ce(20) based on
- linear OA(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 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 OA(4190, 4194329, F4, 23) (dual of [4194329, 4194139, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4191, 4194330, F4, 23) (dual of [4194330, 4194139, 24]-code) | [i] | ||
| 3 | Linear OA(4192, 4194331, F4, 23) (dual of [4194331, 4194139, 24]-code) | [i] | ||
| 4 | Linear OOA(4189, 2097164, F4, 2, 23) (dual of [(2097164, 2), 4194139, 24]-NRT-code) | [i] | OOA Folding | |