Information on Result #681901
Linear OA(4201, 208, F4, 143) (dual of [208, 7, 144]-code), using construction XX applied to C1 = C([0,128]), C2 = C([1,140]), C3 = C1 + C2 = C([1,128]), and C∩ = C1 ∩ C2 = C([0,140]) based on
- linear OA(4183, 189, F4, 131) (dual of [189, 6, 132]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,128], and minimum distance d ≥ |{−2,−1,…,128}|+1 = 132 (BCH-bound) [i]
- linear OA(4185, 189, F4, 140) (dual of [189, 4, 141]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,140], and designed minimum distance d ≥ |I|+1 = 141 [i]
- linear OA(4186, 189, F4, 143) (dual of [189, 3, 144]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,140], and minimum distance d ≥ |{−7,−2,3,…,−53}|+1 = 144 (BCH-bound) [i]
- linear OA(4182, 189, F4, 128) (dual of [189, 7, 129]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,128], and designed minimum distance d ≥ |I|+1 = 129 [i]
- linear OA(42, 3, F4, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
- dual of repetition code with length 3 [i]
- linear OA(413, 16, F4, 11) (dual of [16, 3, 12]-code), using
Mode: Constructive and 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4201, 208, F4, 142) (dual of [208, 7, 143]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4201, 208, F4, 141) (dual of [208, 7, 142]-code) | [i] | ||
| 3 | Linear OA(4200, 207, F4, 142) (dual of [207, 7, 143]-code) | [i] | Truncation | |
| 4 | Linear OA(4198, 205, F4, 140) (dual of [205, 7, 141]-code) | [i] | ||
| 5 | Linear OA(4197, 204, F4, 139) (dual of [204, 7, 140]-code) | [i] | ||
| 6 | Linear OA(4196, 203, F4, 138) (dual of [203, 7, 139]-code) | [i] | ||
| 7 | Linear OA(4195, 202, F4, 137) (dual of [202, 7, 138]-code) | [i] | ||