Information on Result #1603676
Linear OOA(3123, 156140, F3, 4, 16) (dual of [(156140, 4), 624437, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3123, 156140, F3, 3, 16) (dual of [(156140, 3), 468297, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3123, 177151, F3, 3, 16) (dual of [(177151, 3), 531330, 17]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3122, 177151, F3, 3, 16) (dual of [(177151, 3), 531331, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3122, 531453, F3, 16) (dual of [531453, 531331, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3122, 531454, F3, 16) (dual of [531454, 531332, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- 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(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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
- discarding factors / shortening the dual code based on linear OA(3122, 531454, F3, 16) (dual of [531454, 531332, 17]-code), using
- OOA 3-folding [i] based on linear OA(3122, 531453, F3, 16) (dual of [531453, 531331, 17]-code), using
- 31 times duplication [i] based on linear OOA(3122, 177151, F3, 3, 16) (dual of [(177151, 3), 531331, 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(3123, 78069, F3, 20, 16) (dual of [(78069, 20), 1561257, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row |