Information on Result #1532591
Linear OOA(3241, 4357, F3, 3, 44) (dual of [(4357, 3), 12830, 45]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3241, 4357, F3, 44) (dual of [4357, 4116, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, 6594, F3, 44) (dual of [6594, 6353, 45]-code), using
- construction XX applied to Ce(43) ⊂ Ce(39) ⊂ Ce(37) [i] based on
- linear OA(3233, 6561, F3, 44) (dual of [6561, 6328, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(36, 31, F3, 3) (dual of [31, 25, 4]-code or 31-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(43) ⊂ Ce(39) ⊂ Ce(37) [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(3241, 2178, F3, 5, 44) (dual of [(2178, 5), 10649, 45]-NRT-code) | [i] | OOA Folding | |