Information on Result #1298969
Linear OA(3189, 222, F3, 92) (dual of [222, 33, 93]-code), using construction X with Varšamov bound based on
- linear OA(3182, 214, F3, 92) (dual of [214, 32, 93]-code), using
- 30 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
- 30 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3182, 215, F3, 85) (dual of [215, 33, 86]-code), using Gilbert–Varšamov bound and bm = 3182 > Vbs−1(k−1) = 285 434393 699461 772862 687325 369163 726239 928538 294700 595897 460278 674230 737592 462677 727001 [i]
- linear OA(36, 7, F3, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,3)), using
- dual of repetition code with length 7 [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(3189, 222, F3, 91) (dual of [222, 33, 92]-code) | [i] | Strength Reduction | |