Information on Result #1299524
Linear OA(3227, 267, F3, 107) (dual of [267, 40, 108]-code), using construction X with Varšamov bound based on
- linear OA(3224, 262, F3, 107) (dual of [262, 38, 108]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3198, 230, F3, 108) (dual of [230, 32, 109]-code), using
- 14 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
- 14 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3198, 236, F3, 92) (dual of [236, 38, 93]-code), using Gilbert–Varšamov bound and bm = 3198 > Vbs−1(k−1) = 25523 416148 385447 554276 414308 029260 859594 308657 055190 729291 529005 831864 479122 501430 305398 843515 [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(3198, 230, F3, 108) (dual of [230, 32, 109]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3224, 264, F3, 105) (dual of [264, 40, 106]-code), using Gilbert–Varšamov bound and bm = 3224 > Vbs−1(k−1) = 67961 090513 455372 308387 775055 744144 186603 680862 942276 487784 592799 268829 122930 719429 364696 834523 982120 387723 [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(3228, 269, F3, 107) (dual of [269, 41, 108]-code) | [i] | Construction X with Varšamov Bound | |