Information on Result #1299554
Linear OA(3250, 284, F3, 126) (dual of [284, 34, 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, 261, F3, 109) (dual of [261, 34, 110]-code), using Gilbert–Varšamov bound and bm = 3227 > Vbs−1(k−1) = 1 100892 182324 342120 098159 346550 221686 850011 786035 517116 434265 549259 652644 782164 510850 068434 249265 387461 751889 [i]
- linear OA(321, 23, F3, 16) (dual of [23, 2, 17]-code), using
- 1 times truncation [i] based on linear OA(322, 24, F3, 17) (dual of [24, 2, 18]-code), using
- repeating each code word 6 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 6 times [i] based on linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- 1 times truncation [i] based on linear OA(322, 24, F3, 17) (dual of [24, 2, 18]-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(3249, 283, F3, 125) (dual of [283, 34, 126]-code) | [i] | Truncation | |