Information on Result #675642
Linear OA(3203, 6572, F3, 38) (dual of [6572, 6369, 39]-code), using construction XX applied to Ce(37) ⊂ Ce(36) ⊂ Ce(34) based on
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 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
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3203, 3361, F3, 2, 38) (dual of [(3361, 2), 6519, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3203, 3361, F3, 3, 38) (dual of [(3361, 3), 9880, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(3203, 3361, F3, 4, 38) (dual of [(3361, 4), 13241, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(3203, 3361, F3, 5, 38) (dual of [(3361, 5), 16602, 39]-NRT-code) | [i] | ||
| 5 | Digital (165, 203, 3361)-net over F3 | [i] | ||
| 6 | Linear OOA(3203, 3286, F3, 2, 38) (dual of [(3286, 2), 6369, 39]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3203, 1643, F3, 4, 38) (dual of [(1643, 4), 6369, 39]-NRT-code) | [i] | ||