Information on Result #1299501
Linear OA(3247, 281, F3, 125) (dual of [281, 34, 126]-code), using construction X with Varšamov bound based on
- linear OA(3221, 253, F3, 125) (dual of [253, 32, 126]-code), using
- construction X applied to Ce(124) ⊂ Ce(120) [i] based on
- linear OA(3217, 243, F3, 125) (dual of [243, 26, 126]-code), using an extension Ce(124) of 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(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(34, 10, F3, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
- construction X applied to Ce(124) ⊂ Ce(120) [i] based on
- linear OA(3221, 255, F3, 106) (dual of [255, 34, 107]-code), using Gilbert–Varšamov bound and bm = 3221 > Vbs−1(k−1) = 1982 015823 119932 137937 145545 777260 949482 593177 549118 741904 509290 782260 100791 385474 090877 276815 516449 759801 [i]
- linear OA(324, 26, F3, 18) (dual of [26, 2, 19]-code), using
- 2 times truncation [i] based on linear OA(326, 28, F3, 20) (dual of [28, 2, 21]-code), using
- repeating each code word 7 times [i] based on linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- repeating each code word 7 times [i] based on linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- 2 times truncation [i] based on linear OA(326, 28, F3, 20) (dual of [28, 2, 21]-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(3247, 281, F3, 124) (dual of [281, 34, 125]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3248, 282, F3, 125) (dual of [282, 34, 126]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(3246, 280, F3, 124) (dual of [280, 34, 125]-code) | [i] | Truncation | |