Information on Result #1466374
Linear OOA(3189, 4194381, F3, 2, 17) (dual of [(4194381, 2), 8388573, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(323, 80, F3, 2, 8) (dual of [(80, 2), 137, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(323, 80, F3, 8) (dual of [80, 57, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 88, F3, 8) (dual of [88, 65, 9]-code), using
- construction XX applied to Ce(7) ⊂ Ce(6) ⊂ Ce(4) [i] based on
- linear OA(321, 81, F3, 8) (dual of [81, 60, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(317, 81, F3, 7) (dual of [81, 64, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(313, 81, F3, 5) (dual of [81, 68, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(7) ⊂ Ce(6) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(323, 88, F3, 8) (dual of [88, 65, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(323, 80, F3, 8) (dual of [80, 57, 9]-code), using
- linear OOA(3166, 4194301, F3, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-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(3189, 4194381, F3, 3, 17) (dual of [(4194381, 3), 12582954, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3189, 4194381, F3, 4, 17) (dual of [(4194381, 4), 16777335, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(3189, 4194381, F3, 5, 17) (dual of [(4194381, 5), 20971716, 18]-NRT-code) | [i] | ||
| 4 | Digital (172, 189, 4194381)-net over F3 | [i] | ||