Information on Result #677487
Linear OA(357, 260, F3, 16) (dual of [260, 203, 17]-code), using construction XX applied to Ce(15) ⊂ Ce(12) ⊂ Ce(10) based on
- linear OA(351, 243, F3, 16) (dual of [243, 192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(341, 243, F3, 13) (dual of [243, 202, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(336, 243, F3, 11) (dual of [243, 207, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(34, 15, F3, 2) (dual of [15, 11, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(357, 233, F3, 2, 16) (dual of [(233, 2), 409, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(357, 233, F3, 3, 16) (dual of [(233, 3), 642, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(357, 233, F3, 4, 16) (dual of [(233, 4), 875, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(357, 233, F3, 5, 16) (dual of [(233, 5), 1108, 17]-NRT-code) | [i] | ||
| 5 | Digital (41, 57, 233)-net over F3 | [i] | ||