Information on Result #1304645
Linear OA(3165, 2330, F3, 32) (dual of [2330, 2165, 33]-code), using 119 step Varšamov–Edel lengthening with (ri) = (4, 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 7 times 0, 1, 9 times 0, 1, 12 times 0, 1, 17 times 0, 1, 22 times 0, 1, 28 times 0) based on linear OA(3148, 2194, F3, 32) (dual of [2194, 2046, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3141, 2187, F3, 31) (dual of [2187, 2046, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(3165, 2330, F3, 2, 32) (dual of [(2330, 2), 4495, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3165, 2330, F3, 3, 32) (dual of [(2330, 3), 6825, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3165, 2330, F3, 4, 32) (dual of [(2330, 4), 9155, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3165, 2330, F3, 5, 32) (dual of [(2330, 5), 11485, 33]-NRT-code) | [i] | ||
| 5 | Digital (133, 165, 2330)-net over F3 | [i] | ||
| 6 | Linear OOA(3165, 1165, F3, 2, 32) (dual of [(1165, 2), 2165, 33]-NRT-code) | [i] | OOA Folding | |