Information on Result #1299362
Linear OA(3228, 261, F3, 119) (dual of [261, 33, 120]-code), using construction X with Varšamov bound based on
- linear OA(3209, 241, F3, 119) (dual of [241, 32, 120]-code), using
- 3 times truncation [i] 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
- 3 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3209, 242, F3, 100) (dual of [242, 33, 101]-code), using Gilbert–Varšamov bound and bm = 3209 > Vbs−1(k−1) = 3760 661176 767486 618874 860743 251948 747015 179647 073712 568188 938342 678923 135482 108910 140165 246657 955395 [i]
- linear OA(318, 19, F3, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,3)), using
- dual of repetition code with length 19 [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(3228, 261, F3, 118) (dual of [261, 33, 119]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3228, 261, F3, 117) (dual of [261, 33, 118]-code) | [i] | ||
| 3 | Linear OA(3228, 261, F3, 116) (dual of [261, 33, 117]-code) | [i] | ||
| 4 | Linear OA(3228, 261, F3, 115) (dual of [261, 33, 116]-code) | [i] | ||
| 5 | Linear OA(3226, 259, F3, 117) (dual of [259, 33, 118]-code) | [i] | Truncation | |
| 6 | Linear OA(3223, 256, F3, 114) (dual of [256, 33, 115]-code) | [i] | ||
| 7 | Linear OA(3220, 253, F3, 111) (dual of [253, 33, 112]-code) | [i] | ||