Information on Result #1525473
Linear OOA(3168, 4194352, F3, 3, 15) (dual of [(4194352, 3), 12582888, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3168, 4194352, F3, 2, 15) (dual of [(4194352, 2), 8388536, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(318, 51, F3, 2, 7) (dual of [(51, 2), 84, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(318, 51, F3, 7) (dual of [51, 33, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(318, 86, F3, 7) (dual of [86, 68, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(4) [i] based on
- 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(31, 5, F3, 1) (dual of [5, 4, 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(6) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(318, 86, F3, 7) (dual of [86, 68, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(318, 51, F3, 7) (dual of [51, 33, 8]-code), using
- linear OOA(3150, 4194301, F3, 2, 15) (dual of [(4194301, 2), 8388452, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3150, 8388602, F3, 15) (dual of [8388602, 8388452, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- OOA 2-folding [i] based on linear OA(3150, 8388602, F3, 15) (dual of [8388602, 8388452, 16]-code), using
- linear OOA(318, 51, F3, 2, 7) (dual of [(51, 2), 84, 8]-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(3168, 2097176, F3, 5, 15) (dual of [(2097176, 5), 10485712, 16]-NRT-code) | [i] | OOA Folding | |