Information on Result #1299157
Linear OA(3209, 242, F3, 106) (dual of [242, 33, 107]-code), using construction X with Varšamov bound based on
- linear OA(3196, 228, F3, 106) (dual of [228, 32, 107]-code), using
- 16 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
- 16 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3196, 229, F3, 93) (dual of [229, 33, 94]-code), using Gilbert–Varšamov bound and bm = 3196 > Vbs−1(k−1) = 2402 112268 300258 515882 890444 844788 429302 877640 169743 007240 648280 570938 365298 179875 561777 638865 [i]
- linear OA(312, 13, F3, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,3)), using
- dual of repetition code with length 13 [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3209, 242, F3, 105) (dual of [242, 33, 106]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3209, 242, F3, 104) (dual of [242, 33, 105]-code) | [i] | ||
| 3 | Linear OA(3207, 240, F3, 104) (dual of [240, 33, 105]-code) | [i] | Truncation | |
| 4 | Linear OA(3204, 237, F3, 101) (dual of [237, 33, 102]-code) | [i] | ||