Information on Result #689877
Linear OA(963, 6572, F9, 17) (dual of [6572, 6509, 18]-code), using construction XX applied to Ce(16) ⊂ Ce(14) ⊂ Ce(13) based on
- linear OA(961, 6561, F9, 17) (dual of [6561, 6500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(953, 6561, F9, 15) (dual of [6561, 6508, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(949, 6561, F9, 14) (dual of [6561, 6512, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(91, 10, F9, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(963, 6572, F9, 2, 17) (dual of [(6572, 2), 13081, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(963, 6572, F9, 3, 17) (dual of [(6572, 3), 19653, 18]-NRT-code) | [i] | ||
| 3 | Digital (46, 63, 6572)-net over F9 | [i] | ||
| 4 | Linear OOA(963, 3286, F9, 2, 17) (dual of [(3286, 2), 6509, 18]-NRT-code) | [i] | OOA Folding | |