Information on Result #675747
Linear OA(3240, 2203, F3, 51) (dual of [2203, 1963, 52]-code), using construction X applied to C([0,25]) ⊂ C([0,24]) based on
- linear OA(3239, 2188, F3, 51) (dual of [2188, 1949, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,25], and minimum distance d ≥ |{−25,−24,…,25}|+1 = 52 (BCH-bound) [i]
- linear OA(3225, 2188, F3, 49) (dual of [2188, 1963, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,24], and minimum distance d ≥ |{−24,−23,…,24}|+1 = 50 (BCH-bound) [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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
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 OA(3241, 2204, F3, 51) (dual of [2204, 1963, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3242, 2205, F3, 51) (dual of [2205, 1963, 52]-code) | [i] | ||
| 3 | Linear OOA(3240, 1985, F3, 2, 51) (dual of [(1985, 2), 3730, 52]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3240, 1985, F3, 3, 51) (dual of [(1985, 3), 5715, 52]-NRT-code) | [i] | ||
| 5 | Linear OOA(3240, 1985, F3, 4, 51) (dual of [(1985, 4), 7700, 52]-NRT-code) | [i] | ||
| 6 | Linear OOA(3240, 1985, F3, 5, 51) (dual of [(1985, 5), 9685, 52]-NRT-code) | [i] | ||
| 7 | Digital (189, 240, 1985)-net over F3 | [i] | ||
| 8 | Linear OA(3242, 2207, F3, 51) (dual of [2207, 1965, 52]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(3243, 2211, F3, 51) (dual of [2211, 1968, 52]-code) | [i] | ||
| 10 | Linear OA(3244, 2218, F3, 51) (dual of [2218, 1974, 52]-code) | [i] | ||
| 11 | Linear OA(3245, 2230, F3, 51) (dual of [2230, 1985, 52]-code) | [i] | ||
| 12 | Linear OA(3246, 2248, F3, 51) (dual of [2248, 2002, 52]-code) | [i] | ||
| 13 | Linear OA(3247, 2274, F3, 51) (dual of [2274, 2027, 52]-code) | [i] | ||
| 14 | Linear OA(3248, 2308, F3, 51) (dual of [2308, 2060, 52]-code) | [i] | ||
| 15 | Linear OA(3249, 2349, F3, 51) (dual of [2349, 2100, 52]-code) | [i] | ||
| 16 | Linear OA(3250, 2396, F3, 51) (dual of [2396, 2146, 52]-code) | [i] | ||
| 17 | Linear OA(3242, 2206, F3, 51) (dual of [2206, 1964, 52]-code) | [i] | Construction X with Varšamov Bound | |
| 18 | Linear OA(3243, 2208, F3, 51) (dual of [2208, 1965, 52]-code) | [i] | ||
| 19 | Linear OA(3244, 2210, F3, 51) (dual of [2210, 1966, 52]-code) | [i] | ||
| 20 | Linear OOA(3240, 1101, F3, 2, 51) (dual of [(1101, 2), 1962, 52]-NRT-code) | [i] | OOA Folding | |
| 21 | Linear OOA(3240, 734, F3, 3, 51) (dual of [(734, 3), 1962, 52]-NRT-code) | [i] | ||
| 22 | Linear OOA(3240, 550, F3, 4, 51) (dual of [(550, 4), 1960, 52]-NRT-code) | [i] | ||
| 23 | Linear OOA(3240, 440, F3, 5, 51) (dual of [(440, 5), 1960, 52]-NRT-code) | [i] | ||