Information on Result #676247
Linear OA(377, 2208, F3, 16) (dual of [2208, 2131, 17]-code), using construction XX applied to Ce(15) ⊂ Ce(12) ⊂ Ce(10) based on
- linear OA(371, 2187, F3, 16) (dual of [2187, 2116, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(357, 2187, F3, 13) (dual of [2187, 2130, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(350, 2187, F3, 11) (dual of [2187, 2137, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(34, 19, F3, 2) (dual of [19, 15, 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(377, 1164, F3, 2, 16) (dual of [(1164, 2), 2251, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(377, 1164, F3, 3, 16) (dual of [(1164, 3), 3415, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(377, 1164, F3, 4, 16) (dual of [(1164, 4), 4579, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(377, 1164, F3, 5, 16) (dual of [(1164, 5), 5743, 17]-NRT-code) | [i] | ||
| 5 | Digital (61, 77, 1164)-net over F3 | [i] | ||
| 6 | Linear OOA(377, 1104, F3, 2, 16) (dual of [(1104, 2), 2131, 17]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(377, 736, F3, 3, 16) (dual of [(736, 3), 2131, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(377, 552, F3, 4, 16) (dual of [(552, 4), 2131, 17]-NRT-code) | [i] | ||