Information on Result #1522070
Linear OOA(3105, 598554, F3, 3, 12) (dual of [(598554, 3), 1795557, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3105, 598554, F3, 2, 12) (dual of [(598554, 2), 1197003, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3105, 797168, F3, 2, 12) (dual of [(797168, 2), 1594231, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3105, 1594336, F3, 12) (dual of [1594336, 1594231, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3105, 1594337, F3, 12) (dual of [1594337, 1594232, 13]-code), using
- 1 times truncation [i] based on linear OA(3106, 1594338, F3, 13) (dual of [1594338, 1594232, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [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(392, 1594323, F3, 11) (dual of [1594323, 1594231, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(314, 15, F3, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,3)), using
- dual of repetition code with length 15 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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(10) [i] based on
- 1 times truncation [i] based on linear OA(3106, 1594338, F3, 13) (dual of [1594338, 1594232, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3105, 1594337, F3, 12) (dual of [1594337, 1594232, 13]-code), using
- OOA 2-folding [i] based on linear OA(3105, 1594336, F3, 12) (dual of [1594336, 1594231, 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(3105, 299276, F3, 15, 12) (dual of [(299276, 15), 4489035, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |