Information on Result #674264
Linear OA(3114, 4782985, F3, 13) (dual of [4782985, 4782871, 14]-code), using construction X4 applied to Ce(12) ⊂ Ce(10) based on
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 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(3115, 4782986, F3, 13) (dual of [4782986, 4782871, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3116, 4782987, F3, 13) (dual of [4782987, 4782871, 14]-code) | [i] | ||
| 3 | Linear OA(3113, 4782984, F3, 12) (dual of [4782984, 4782871, 13]-code) | [i] | Truncation | |
| 4 | Linear OOA(3114, 956597, F3, 5, 13) (dual of [(956597, 5), 4782871, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3114, 797164, F3, 13, 13) (dual of [(797164, 13), 10363018, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |