Information on Result #1299069
Linear OA(3203, 238, F3, 98) (dual of [238, 35, 99]-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, 225, F3, 89) (dual of [225, 35, 90]-code), using Gilbert–Varšamov bound and bm = 3190 > Vbs−1(k−1) = 3 744826 549838 190067 018039 170197 407563 989371 106591 819567 859976 652957 848106 356670 494671 041921 [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(3202, 237, F3, 97) (dual of [237, 35, 98]-code) | [i] | Truncation | |