Information on Result #689255
Linear OA(987, 531456, F9, 16) (dual of [531456, 531369, 17]-code), using construction XX applied to Ce(15) ⊂ Ce(13) ⊂ Ce(12) based on
- linear OA(985, 531441, F9, 16) (dual of [531441, 531356, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(973, 531441, F9, 14) (dual of [531441, 531368, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(967, 531441, F9, 13) (dual of [531441, 531374, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(91, 14, F9, 1) (dual of [14, 13, 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(987, 531456, F9, 2, 16) (dual of [(531456, 2), 1062825, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(987, 531456, F9, 3, 16) (dual of [(531456, 3), 1594281, 17]-NRT-code) | [i] | ||
| 3 | Digital (71, 87, 531456)-net over F9 | [i] | ||
| 4 | Linear OOA(987, 265728, F9, 2, 16) (dual of [(265728, 2), 531369, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(987, 177152, F9, 3, 16) (dual of [(177152, 3), 531369, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(987, 66432, F9, 16, 16) (dual of [(66432, 16), 1062825, 17]-NRT-code) | [i] | OA Folding and Stacking | |