Information on Result #676069
Linear OA(3214, 2223, F3, 44) (dual of [2223, 2009, 45]-code), using construction X applied to Ce(43) ⊂ Ce(37) based on
- linear OA(3204, 2187, F3, 44) (dual of [2187, 1983, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3176, 2187, F3, 38) (dual of [2187, 2011, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 12, F3, 1) (dual of [12, 11, 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(33, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
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(3214, 2131, F3, 2, 44) (dual of [(2131, 2), 4048, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3214, 2131, F3, 3, 44) (dual of [(2131, 3), 6179, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(3214, 2131, F3, 4, 44) (dual of [(2131, 4), 8310, 45]-NRT-code) | [i] | ||
| 4 | Linear OOA(3214, 2131, F3, 5, 44) (dual of [(2131, 5), 10441, 45]-NRT-code) | [i] | ||
| 5 | Digital (170, 214, 2131)-net over F3 | [i] | ||
| 6 | Linear OOA(3214, 741, F3, 3, 44) (dual of [(741, 3), 2009, 45]-NRT-code) | [i] | OOA Folding | |