Information on Result #1532220
Linear OOA(3238, 4194372, F3, 3, 21) (dual of [(4194372, 3), 12582878, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3238, 4194372, F3, 2, 21) (dual of [(4194372, 2), 8388506, 22]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(328, 71, F3, 2, 10) (dual of [(71, 2), 114, 11]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(328, 71, F3, 10) (dual of [71, 43, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(328, 92, F3, 10) (dual of [92, 64, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(325, 81, F3, 10) (dual of [81, 56, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(33, 11, F3, 2) (dual of [11, 8, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(328, 92, F3, 10) (dual of [92, 64, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(328, 71, F3, 10) (dual of [71, 43, 11]-code), using
- linear OOA(3210, 4194301, F3, 2, 21) (dual of [(4194301, 2), 8388392, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3210, 8388602, F3, 21) (dual of [8388602, 8388392, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- OOA 2-folding [i] based on linear OA(3210, 8388602, F3, 21) (dual of [8388602, 8388392, 22]-code), using
- linear OOA(328, 71, F3, 2, 10) (dual of [(71, 2), 114, 11]-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(3238, 2097186, F3, 5, 21) (dual of [(2097186, 5), 10485692, 22]-NRT-code) | [i] | OOA Folding | |