Information on Result #1299017
Linear OA(3199, 234, F3, 96) (dual of [234, 35, 97]-code), using construction X with Varšamov bound based on
- linear OA(3186, 218, F3, 96) (dual of [218, 32, 97]-code), using
- 26 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
- 26 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3186, 221, F3, 87) (dual of [221, 35, 88]-code), using Gilbert–Varšamov bound and bm = 3186 > Vbs−1(k−1) = 53489 045246 448242 269515 969794 074412 174117 934163 760202 167984 522628 521399 794236 397041 288753 [i]
- linear OA(310, 13, F3, 8) (dual of [13, 3, 9]-code), using
- Simplex code S(3,3) [i]
- the expurgated narrow-sense BCH-code C(I) with length 13 | 33−1, defining interval I = [0,6], and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [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(3199, 234, F3, 95) (dual of [234, 35, 96]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3196, 231, F3, 93) (dual of [231, 35, 94]-code) | [i] | Truncation | |
| 3 | Linear OA(3203, 240, F3, 96) (dual of [240, 37, 97]-code) | [i] | Construction X with Varšamov Bound | |