Information on Result #1522152
Linear OOA(3107, 764067, F3, 3, 12) (dual of [(764067, 3), 2292094, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3107, 764067, F3, 2, 12) (dual of [(764067, 2), 1528027, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3107, 797176, F3, 2, 12) (dual of [(797176, 2), 1594245, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3107, 1594352, F3, 12) (dual of [1594352, 1594245, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3106, 1594351, F3, 12) (dual of [1594351, 1594245, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(3105, 1594323, F3, 13) (dual of [1594323, 1594218, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(327, 28, F3, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
- dual of repetition code with length 28 [i]
- linear OA(31, 28, F3, 1) (dual of [28, 27, 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
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3106, 1594351, F3, 12) (dual of [1594351, 1594245, 13]-code), using
- OOA 2-folding [i] based on linear OA(3107, 1594352, F3, 12) (dual of [1594352, 1594245, 13]-code), using
Mode: 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(3107, 382033, F3, 5, 12) (dual of [(382033, 5), 1910058, 13]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3107, 382033, F3, 15, 12) (dual of [(382033, 15), 5730388, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |