Information on Result #1602673
Linear OOA(3100, 1594328, F3, 4, 11) (dual of [(1594328, 4), 6377212, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3100, 1594328, F3, 3, 11) (dual of [(1594328, 3), 4782884, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3100, 4782984, F3, 11) (dual of [4782984, 4782884, 12]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(3100, 4782985, F3, 11) (dual of [4782985, 4782885, 12]-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(3101, 1594328, F3, 4, 11) (dual of [(1594328, 4), 6377211, 12]-NRT-code) | [i] | OOA Duplication | |