Information on Result #1299512
Linear OA(3225, 265, F3, 106) (dual of [265, 40, 107]-code), using construction X with Varšamov bound based on
- linear OA(3222, 260, F3, 106) (dual of [260, 38, 107]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3196, 228, F3, 106) (dual of [228, 32, 107]-code), using
- 16 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
- 16 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3196, 234, F3, 91) (dual of [234, 38, 92]-code), using Gilbert–Varšamov bound and bm = 3196 > Vbs−1(k−1) = 3035 396854 494141 386284 102043 906786 923449 453164 313656 486040 182425 457622 204865 129493 388771 589475 [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(3196, 228, F3, 106) (dual of [228, 32, 107]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3222, 262, F3, 104) (dual of [262, 40, 105]-code), using Gilbert–Varšamov bound and bm = 3222 > Vbs−1(k−1) = 8141 397532 072701 044117 734084 441803 732262 940677 268150 808345 805289 753868 022932 956597 639377 743797 779684 629747 [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(3226, 267, F3, 106) (dual of [267, 41, 107]-code) | [i] | Construction X with Varšamov Bound | |