Information on Result #1415914
Linear OOA(3212, 2407, F3, 2, 42) (dual of [(2407, 2), 4602, 43]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3212, 2407, F3, 42) (dual of [2407, 2195, 43]-code), using
- 191 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 7 times 0, 1, 11 times 0, 1, 16 times 0, 1, 23 times 0, 1, 29 times 0, 1, 38 times 0, 1, 46 times 0) [i] based on linear OA(3198, 2202, F3, 42) (dual of [2202, 2004, 43]-code), using
- construction X applied to Ce(42) ⊂ Ce(39) [i] based on
- linear OA(3197, 2187, F3, 43) (dual of [2187, 1990, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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(42) ⊂ Ce(39) [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(3212, 1203, F3, 3, 42) (dual of [(1203, 3), 3397, 43]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3212, 1203, F3, 4, 42) (dual of [(1203, 4), 4600, 43]-NRT-code) | [i] | ||