Information on Result #812929
Linear OOA(386, 29538, F3, 2, 12) (dual of [(29538, 2), 58990, 13]-NRT-code), using OOA 2-folding based on linear OA(386, 59076, F3, 12) (dual of [59076, 58990, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(386, 59077, F3, 12) (dual of [59077, 58991, 13]-code), using
- construction XX applied to Ce(12) ⊂ Ce(9) ⊂ Ce(7) [i] based on
- linear OA(381, 59049, F3, 13) (dual of [59049, 58968, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(361, 59049, F3, 10) (dual of [59049, 58988, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(351, 59049, F3, 8) (dual of [59049, 58998, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 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
- linear OA(31, 4, F3, 1) (dual of [4, 3, 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 (see above)
- construction XX applied to Ce(12) ⊂ Ce(9) ⊂ Ce(7) [i] based on
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 OOA(386, 29538, F3, 3, 12) (dual of [(29538, 3), 88528, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(386, 29538, F3, 4, 12) (dual of [(29538, 4), 118066, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(386, 29538, F3, 5, 12) (dual of [(29538, 5), 147604, 13]-NRT-code) | [i] | ||
| 4 | Digital (74, 86, 29538)-net over F3 | [i] | ||