Information on Result #1604245
Linear OOA(3134, 427458, F3, 4, 16) (dual of [(427458, 4), 1709698, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3134, 427458, F3, 3, 16) (dual of [(427458, 3), 1282240, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3134, 531446, F3, 3, 16) (dual of [(531446, 3), 1594204, 17]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3133, 531446, F3, 3, 16) (dual of [(531446, 3), 1594205, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3133, 1594338, F3, 16) (dual of [1594338, 1594205, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3132, 1594337, F3, 16) (dual of [1594337, 1594205, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3118, 1594323, F3, 14) (dual of [1594323, 1594205, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3132, 1594337, F3, 16) (dual of [1594337, 1594205, 17]-code), using
- OOA 3-folding [i] based on linear OA(3133, 1594338, F3, 16) (dual of [1594338, 1594205, 17]-code), using
- 31 times duplication [i] based on linear OOA(3133, 531446, F3, 3, 16) (dual of [(531446, 3), 1594205, 17]-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(3134, 213728, F3, 20, 16) (dual of [(213728, 20), 4274426, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |