Information on Result #1605054
Linear OOA(3149, 1849542, F3, 4, 15) (dual of [(1849542, 4), 7398019, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3149, 1849542, F3, 2, 15) (dual of [(1849542, 2), 3698935, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3149, 2391509, F3, 2, 15) (dual of [(2391509, 2), 4782869, 16]-NRT-code), using
- 1 step truncation [i] based on linear OOA(3150, 2391510, F3, 2, 16) (dual of [(2391510, 2), 4782870, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3150, 4783020, F3, 16) (dual of [4783020, 4782870, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- 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(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(39, 51, F3, 4) (dual of [51, 42, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(3150, 4783020, F3, 16) (dual of [4783020, 4782870, 17]-code), using
- 1 step truncation [i] based on linear OOA(3150, 2391510, F3, 2, 16) (dual of [(2391510, 2), 4782870, 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(3149, 924770, F3, 20, 15) (dual of [(924770, 20), 18495251, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |