Information on Result #1412851
Linear OOA(3173, 1723, F3, 2, 36) (dual of [(1723, 2), 3273, 37]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3173, 1723, F3, 36) (dual of [1723, 1550, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3173, 2207, F3, 36) (dual of [2207, 2034, 37]-code), using
- construction XX applied to Ce(36) ⊂ Ce(33) ⊂ Ce(31) [i] based on
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 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
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [i]
- construction XX applied to Ce(36) ⊂ Ce(33) ⊂ Ce(31) [i] based on
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(3173, 861, F3, 3, 36) (dual of [(861, 3), 2410, 37]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3173, 861, F3, 4, 36) (dual of [(861, 4), 3271, 37]-NRT-code) | [i] | ||