Information on Result #674529
Linear OA(3133, 531453, F3, 17) (dual of [531453, 531320, 18]-code), using construction X applied to Ce(16) ⊂ Ce(15) based on
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 12, F3, 0) (dual of [12, 12, 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: 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 OA(3134, 531454, F3, 17) (dual of [531454, 531320, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3135, 531455, F3, 17) (dual of [531455, 531320, 18]-code) | [i] | ||
| 3 | Linear OA(3136, 531456, F3, 17) (dual of [531456, 531320, 18]-code) | [i] | ||
| 4 | Linear OOA(3133, 265726, F3, 2, 17) (dual of [(265726, 2), 531319, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(3133, 177151, F3, 3, 17) (dual of [(177151, 3), 531320, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(3133, 132863, F3, 4, 17) (dual of [(132863, 4), 531319, 18]-NRT-code) | [i] | ||
| 7 | Linear OOA(3133, 106290, F3, 5, 17) (dual of [(106290, 5), 531317, 18]-NRT-code) | [i] | ||
| 8 | Linear OOA(3133, 66431, F3, 17, 17) (dual of [(66431, 17), 1129194, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |