Information on Result #1299065
Linear OA(3200, 233, F3, 100) (dual of [233, 33, 101]-code), using construction X with Varšamov bound based on
- linear OA(3190, 222, F3, 100) (dual of [222, 32, 101]-code), using
- 22 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
- 22 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3190, 223, F3, 90) (dual of [223, 33, 91]-code), using Gilbert–Varšamov bound and bm = 3190 > Vbs−1(k−1) = 4 210751 041745 256195 657641 017337 263880 726864 841194 966348 802686 818282 881080 769917 916622 174137 [i]
- linear OA(39, 10, F3, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,3)), using
- dual of repetition code with length 10 [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(3200, 233, F3, 99) (dual of [233, 33, 100]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3200, 233, F3, 98) (dual of [233, 33, 99]-code) | [i] | ||
| 3 | Linear OA(3197, 230, F3, 97) (dual of [230, 33, 98]-code) | [i] | Truncation | |
| 4 | Linear OA(3194, 227, F3, 94) (dual of [227, 33, 95]-code) | [i] | ||