Information on Result #1299553
Linear OA(3243, 276, F3, 126) (dual of [276, 33, 127]-code), using construction X with Varšamov bound based on
- linear OA(3227, 259, F3, 126) (dual of [259, 32, 127]-code), using
- construction XX applied to C1 = C([239,120]), C2 = C([1,124]), C3 = C1 + C2 = C([1,120]), and C∩ = C1 ∩ C2 = C([239,124]) [i] based on
- linear OA(3216, 242, F3, 124) (dual of [242, 26, 125]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,120}, and designed minimum distance d ≥ |I|+1 = 125 [i]
- linear OA(3216, 242, F3, 124) (dual of [242, 26, 125]-code), using the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,124], and designed minimum distance d ≥ |I|+1 = 125 [i]
- linear OA(3222, 242, F3, 128) (dual of [242, 20, 129]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−3,−2,…,124}, and designed minimum distance d ≥ |I|+1 = 129 [i]
- linear OA(3210, 242, F3, 120) (dual of [242, 32, 121]-code), using 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(31, 7, F3, 1) (dual of [7, 6, 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
- linear OA(34, 10, F3, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
- construction XX applied to C1 = C([239,120]), C2 = C([1,124]), C3 = C1 + C2 = C([1,120]), and C∩ = C1 ∩ C2 = C([239,124]) [i] based on
- linear OA(3227, 260, F3, 110) (dual of [260, 33, 111]-code), using Gilbert–Varšamov bound and bm = 3227 > Vbs−1(k−1) = 1 804891 280571 756437 605753 588366 843920 690513 367689 580110 251197 488857 615662 393696 450531 115381 438705 851867 708443 [i]
- linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
- dual of repetition code with length 16 [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(3243, 276, F3, 125) (dual of [276, 33, 126]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3243, 276, F3, 124) (dual of [276, 33, 125]-code) | [i] | ||
| 3 | Linear OA(3242, 275, F3, 125) (dual of [275, 33, 126]-code) | [i] | Truncation | |
| 4 | Linear OA(3241, 274, F3, 124) (dual of [274, 33, 125]-code) | [i] | ||
| 5 | Linear OA(3239, 272, F3, 122) (dual of [272, 33, 123]-code) | [i] | ||