Information on Result #1299113
Linear OA(3219, 258, F3, 103) (dual of [258, 39, 104]-code), using construction X with Varšamov bound based on
- linear OA(3193, 225, F3, 103) (dual of [225, 32, 104]-code), using
- 19 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
- 19 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3193, 232, F3, 89) (dual of [232, 39, 90]-code), using Gilbert–Varšamov bound and bm = 3193 > Vbs−1(k−1) = 111 341177 112139 333023 099013 757747 724050 500059 056552 108492 378435 254675 961803 239844 185922 557195 [i]
- linear OA(319, 26, F3, 13) (dual of [26, 7, 14]-code), using
- contraction [i] based on linear OA(345, 52, F3, 27) (dual of [52, 7, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,25], and minimum distance d ≥ |{−1,0,…,25}|+1 = 28 (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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3220, 260, F3, 103) (dual of [260, 40, 104]-code) | [i] | Construction X with Varšamov Bound | |