Information on Result #677781
Linear OA(372, 88, F3, 43) (dual of [88, 16, 44]-code), using construction XX applied to Ce(43) ⊂ Ce(40) ⊂ Ce(39) based on
- linear OA(370, 81, F3, 44) (dual of [81, 11, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(366, 81, F3, 41) (dual of [81, 15, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(365, 81, F3, 40) (dual of [81, 16, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(372, 88, F3, 42) (dual of [88, 16, 43]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(372, 88, F3, 41) (dual of [88, 16, 42]-code) | [i] | ||
| 3 | Linear OA(372, 88, F3, 40) (dual of [88, 16, 41]-code) | [i] | ||
| 4 | Linear OA(372, 88, F3, 39) (dual of [88, 16, 40]-code) | [i] | ||
| 5 | Linear OA(372, 88, F3, 38) (dual of [88, 16, 39]-code) | [i] | ||
| 6 | Linear OA(372, 88, F3, 37) (dual of [88, 16, 38]-code) | [i] | ||
| 7 | Linear OA(372, 88, F3, 36) (dual of [88, 16, 37]-code) | [i] | ||
| 8 | Linear OA(376, 92, F3, 43) (dual of [92, 16, 44]-code) | [i] | Code Embedding in Larger Space | |
| 9 | Linear OA(370, 86, F3, 41) (dual of [86, 16, 42]-code) | [i] | Truncation | |
| 10 | Linear OA(369, 85, F3, 40) (dual of [85, 16, 41]-code) | [i] | ||
| 11 | Linear OA(368, 84, F3, 39) (dual of [84, 16, 40]-code) | [i] | ||
| 12 | Linear OA(367, 83, F3, 38) (dual of [83, 16, 39]-code) | [i] | ||
| 13 | Linear OA(3154, 170, F3, 85) (dual of [170, 16, 86]-code) | [i] | Juxtaposition | |
| 14 | Linear OA(381, 98, F3, 43) (dual of [98, 17, 44]-code) | [i] | Construction X with Varšamov Bound | |
| 15 | Linear OOA(372, 44, F3, 2, 43) (dual of [(44, 2), 16, 44]-NRT-code) | [i] | OOA Folding | |
| 16 | Linear OOA(372, 22, F3, 4, 43) (dual of [(22, 4), 16, 44]-NRT-code) | [i] | ||