Information on Result #1605529
Linear OOA(3157, 1271815, F3, 4, 17) (dual of [(1271815, 4), 5087103, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3157, 1271815, F3, 3, 17) (dual of [(1271815, 3), 3815288, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3157, 1594328, F3, 3, 17) (dual of [(1594328, 3), 4782827, 18]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3156, 1594328, F3, 3, 17) (dual of [(1594328, 3), 4782828, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3156, 4782984, F3, 17) (dual of [4782984, 4782828, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3155, 4782983, F3, 17) (dual of [4782983, 4782828, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 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
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3155, 4782983, F3, 17) (dual of [4782983, 4782828, 18]-code), using
- OOA 3-folding [i] based on linear OA(3156, 4782984, F3, 17) (dual of [4782984, 4782828, 18]-code), using
- 31 times duplication [i] based on linear OOA(3156, 1594328, F3, 3, 17) (dual of [(1594328, 3), 4782828, 18]-NRT-code), 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(3157, 635907, F3, 20, 17) (dual of [(635907, 20), 12717983, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |