Information on Result #677778
Linear OA(387, 103, F3, 50) (dual of [103, 16, 51]-code), using construction XX applied to Ce(49) ⊂ Ce(40) ⊂ Ce(39) based on
- linear OA(374, 81, F3, 50) (dual of [81, 7, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [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(312, 21, F3, 8) (dual of [21, 9, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(312, 24, F3, 8) (dual of [24, 12, 9]-code), using
- extended quadratic residue code Qe(24,3) [i]
- discarding factors / shortening the dual code based on linear OA(312, 24, F3, 8) (dual of [24, 12, 9]-code), 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(387, 103, F3, 49) (dual of [103, 16, 50]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(387, 103, F3, 48) (dual of [103, 16, 49]-code) | [i] | ||
| 3 | Linear OA(387, 103, F3, 47) (dual of [103, 16, 48]-code) | [i] | ||
| 4 | Linear OA(387, 103, F3, 46) (dual of [103, 16, 47]-code) | [i] | ||
| 5 | Linear OA(388, 104, F3, 50) (dual of [104, 16, 51]-code) | [i] | Code Embedding in Larger Space | |
| 6 | Linear OA(390, 106, F3, 50) (dual of [106, 16, 51]-code) | [i] | ||
| 7 | Linear OA(384, 100, F3, 47) (dual of [100, 16, 48]-code) | [i] | Truncation | |
| 8 | Linear OA(378, 94, F3, 41) (dual of [94, 16, 42]-code) | [i] | ||
| 9 | Linear OA(377, 93, F3, 40) (dual of [93, 16, 41]-code) | [i] | ||
| 10 | Linear OA(376, 92, F3, 39) (dual of [92, 16, 40]-code) | [i] | ||
| 11 | Linear OA(3105, 126, F3, 50) (dual of [126, 21, 51]-code) | [i] | Construction X with Varšamov Bound | |
| 12 | Linear OA(3103, 124, F3, 49) (dual of [124, 21, 50]-code) | [i] | ||