Information on Result #731718
Linear OA(2196, 210, F2, 95) (dual of [210, 14, 96]-code), using concatenation of two codes based on
- linear OA(463, 70, F4, 47) (dual of [70, 7, 48]-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]) [i] based on
- linear OA(457, 63, F4, 43) (dual of [63, 6, 44]-code), using contraction [i] 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(459, 63, F4, 46) (dual of [63, 4, 47]-code), using contraction [i] based on 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(460, 63, F4, 47) (dual of [63, 3, 48]-code), using contraction [i] based on 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(456, 63, F4, 42) (dual of [63, 7, 43]-code), using contraction [i] based on 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(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), 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]) [i] based on
- linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(2196, 210, F2, 94) (dual of [210, 14, 95]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2197, 211, F2, 95) (dual of [211, 14, 96]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2195, 209, F2, 94) (dual of [209, 14, 95]-code) | [i] | Truncation | |
| 4 | Linear OA(2194, 208, F2, 93) (dual of [208, 14, 94]-code) | [i] | ||
| 5 | Linear OA(2101, 114, F2, 47) (dual of [114, 13, 48]-code) | [i] | Residual Code | |
| 6 | Linear OOA(2196, 105, F2, 2, 95) (dual of [(105, 2), 14, 96]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2196, 70, F2, 3, 95) (dual of [(70, 3), 14, 96]-NRT-code) | [i] | ||
| 8 | Linear OOA(2196, 42, F2, 5, 95) (dual of [(42, 5), 14, 96]-NRT-code) | [i] | ||