Information on Result #953059
Linear OOA(3192, 531461, F3, 3, 21) (dual of [(531461, 3), 1594191, 22]-NRT-code), using OOA 3-folding based on linear OA(3192, 1594383, F3, 21) (dual of [1594383, 1594191, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3192, 1594384, F3, 21) (dual of [1594384, 1594192, 22]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3183, 1594323, F3, 22) (dual of [1594323, 1594140, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(39, 61, F3, 4) (dual of [61, 52, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
Mode: Constructive and 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(3192, 531461, F3, 4, 21) (dual of [(531461, 4), 2125652, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3192, 531461, F3, 5, 21) (dual of [(531461, 5), 2657113, 22]-NRT-code) | [i] | ||
| 3 | Digital (171, 192, 531461)-net over F3 | [i] | ||