Information on Result #1299418
Linear OA(3233, 266, F3, 122) (dual of [266, 33, 123]-code), using construction X with Varšamov bound based on
- linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- construction X applied to Ce(121) ⊂ Ce(120) [i] based on
- linear OA(3212, 243, F3, 122) (dual of [243, 31, 123]-code), using an extension Ce(121) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,121], and designed minimum distance d ≥ |I|+1 = 122 [i]
- linear OA(3211, 243, F3, 121) (dual of [243, 32, 122]-code), using an extension Ce(120) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,120], and designed minimum distance d ≥ |I|+1 = 121 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(121) ⊂ Ce(120) [i] based on
- linear OA(3212, 245, F3, 101) (dual of [245, 33, 102]-code), using Gilbert–Varšamov bound and bm = 3212 > Vbs−1(k−1) = 52308 427754 299535 795210 347183 684719 154682 108255 881852 769694 371030 608856 693336 029023 147394 713675 737361 [i]
- linear OA(320, 21, F3, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,3)), using
- dual of repetition code with length 21 [i]
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 OA(3233, 266, F3, 121) (dual of [266, 33, 122]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3233, 266, F3, 120) (dual of [266, 33, 121]-code) | [i] | ||
| 3 | Linear OA(3233, 266, F3, 119) (dual of [266, 33, 120]-code) | [i] | ||
| 4 | Linear OA(3233, 266, F3, 118) (dual of [266, 33, 119]-code) | [i] | ||
| 5 | Linear OA(3234, 267, F3, 122) (dual of [267, 33, 123]-code) | [i] | Code Embedding in Larger Space | |
| 6 | Linear OA(3232, 265, F3, 121) (dual of [265, 33, 122]-code) | [i] | Truncation | |
| 7 | Linear OA(3229, 262, F3, 118) (dual of [262, 33, 119]-code) | [i] | ||
| 8 | Linear OA(3226, 259, F3, 115) (dual of [259, 33, 116]-code) | [i] | ||
| 9 | Linear OA(3223, 256, F3, 112) (dual of [256, 33, 113]-code) | [i] | ||