Information on Result #674534
Linear OA(398, 531455, F3, 13) (dual of [531455, 531357, 14]-code), using construction X4 applied to Ce(12) ⊂ Ce(10) based on
- linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(385, 531441, F3, 11) (dual of [531441, 531356, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(313, 14, F3, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
- dual of repetition code with length 14 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 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(399, 531456, F3, 13) (dual of [531456, 531357, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3100, 531457, F3, 13) (dual of [531457, 531357, 14]-code) | [i] | ||
| 3 | Linear OA(397, 531454, F3, 12) (dual of [531454, 531357, 13]-code) | [i] | Truncation | |
| 4 | Linear OOA(398, 106291, F3, 5, 13) (dual of [(106291, 5), 531357, 14]-NRT-code) | [i] | OOA Folding | |