Information on Result #1299200
Linear OA(3224, 261, F3, 108) (dual of [261, 37, 109]-code), using construction X with Varšamov bound based on
- linear OA(3199, 231, F3, 109) (dual of [231, 32, 110]-code), using
- 13 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
- 13 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3199, 236, F3, 93) (dual of [236, 37, 94]-code), using Gilbert–Varšamov bound and bm = 3199 > Vbs−1(k−1) = 80548 836024 628341 911135 343935 330744 480150 514063 413492 458614 552502 229622 395986 985221 020596 693115 [i]
- linear OA(320, 25, F3, 14) (dual of [25, 5, 15]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(320, 26, F3, 14) (dual of [26, 6, 15]-code), 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(3223, 260, F3, 107) (dual of [260, 37, 108]-code) | [i] | Truncation | |