Information on Result #1642292
Linear OOA(3102, 1732503, F3, 5, 11) (dual of [(1732503, 5), 8662413, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3102, 1732503, F3, 2, 11) (dual of [(1732503, 2), 3464904, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3102, 2391493, F3, 2, 11) (dual of [(2391493, 2), 4782884, 12]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3101, 2391493, F3, 2, 11) (dual of [(2391493, 2), 4782885, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3101, 4782986, F3, 11) (dual of [4782986, 4782885, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3100, 4782985, F3, 11) (dual of [4782985, 4782885, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(9) [i] based on
- 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(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [i]
- linear OA(31, 16, F3, 1) (dual of [16, 15, 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 X4 applied to Ce(10) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3100, 4782985, F3, 11) (dual of [4782985, 4782885, 12]-code), using
- OOA 2-folding [i] based on linear OA(3101, 4782986, F3, 11) (dual of [4782986, 4782885, 12]-code), using
- 31 times duplication [i] based on linear OOA(3101, 2391493, F3, 2, 11) (dual of [(2391493, 2), 4782885, 12]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3102, 1732502, F3, 15, 11) (dual of [(1732502, 15), 25987428, 12]-NRT-code) | [i] | OOA Stacking with Additional Row | |