Information on Result #1299558
Linear OA(3231, 271, F3, 109) (dual of [271, 40, 110]-code), using construction X with Varšamov bound based on
- linear OA(3228, 266, F3, 109) (dual of [266, 38, 110]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3202, 234, F3, 112) (dual of [234, 32, 113]-code), using
- 10 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
- 10 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3202, 240, F3, 94) (dual of [240, 38, 95]-code), using Gilbert–Varšamov bound and bm = 3202 > Vbs−1(k−1) = 1 799868 842869 833972 072835 754710 234813 588084 275502 380060 973810 565688 930714 833338 841591 279369 490155 [i]
- linear OA(320, 26, F3, 14) (dual of [26, 6, 15]-code), using
- contraction [i] based on linear OA(346, 52, F3, 29) (dual of [52, 6, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,27], and minimum distance d ≥ |{−1,0,…,27}|+1 = 30 (BCH-bound) [i]
- linear OA(3202, 234, F3, 112) (dual of [234, 32, 113]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3228, 268, F3, 107) (dual of [268, 40, 108]-code), using Gilbert–Varšamov bound and bm = 3228 > Vbs−1(k−1) = 4 726167 078855 164899 128712 308306 667303 000750 226436 106399 833618 200807 346301 574509 701240 294462 548839 387948 249083 [i]
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(3232, 273, F3, 109) (dual of [273, 41, 110]-code) | [i] | Construction X with Varšamov Bound | |