Information on Result #1529700
Linear OOA(3216, 4303, F3, 3, 39) (dual of [(4303, 3), 12693, 40]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3216, 4303, F3, 39) (dual of [4303, 4087, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, 6593, F3, 39) (dual of [6593, 6377, 40]-code), using
- construction XX applied to Ce(39) ⊂ Ce(34) ⊂ Ce(33) [i] based on
- 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(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(39) ⊂ Ce(34) ⊂ Ce(33) [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(3216, 2151, F3, 5, 39) (dual of [(2151, 5), 10539, 40]-NRT-code) | [i] | OOA Folding | |