Information on Result #2235387
Linear OA(444, 50, F4, 32) (dual of [50, 6, 33]-code), using 3 times truncation based on linear OA(447, 53, F4, 35) (dual of [53, 6, 36]-code), using
- construction XX applied to C1 = C([0,101]), C2 = C([1,104]), C3 = C1 + C2 = C([1,101]), and C∩ = C1 ∩ C2 = C([0,104]) [i] based on
- linear OA(446, 51, F4, 34) (dual of [51, 5, 35]-code), using contraction [i] based on linear OA(4148, 153, F4, 104) (dual of [153, 5, 105]-code), using the expurgated narrow-sense BCH-code C(I) with length 153 | 412−1, defining interval I = [0,101], and minimum distance d ≥ |{−2,−1,…,101}|+1 = 105 (BCH-bound) [i]
- linear OA(446, 51, F4, 34) (dual of [51, 5, 35]-code), using contraction [i] based on linear OA(4148, 153, F4, 104) (dual of [153, 5, 105]-code), using the narrow-sense BCH-code C(I) with length 153 | 412−1, defining interval I = [1,104], and designed minimum distance d ≥ |I|+1 = 105 [i]
- linear OA(447, 51, F4, 35) (dual of [51, 4, 36]-code), using contraction [i] based on linear OA(4149, 153, F4, 107) (dual of [153, 4, 108]-code), using the expurgated narrow-sense BCH-code C(I) with length 153 | 412−1, defining interval I = [0,104], and minimum distance d ≥ |{−2,−1,…,104}|+1 = 108 (BCH-bound) [i]
- linear OA(445, 51, F4, 33) (dual of [51, 6, 34]-code), using contraction [i] based on linear OA(4147, 153, F4, 101) (dual of [153, 6, 102]-code), using the narrow-sense BCH-code C(I) with length 153 | 412−1, defining interval I = [1,101], and designed minimum distance d ≥ |I|+1 = 102 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code) (see above)
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(4124, 130, F4, 88) (dual of [130, 6, 89]-code) | [i] | Juxtaposition | |
| 2 | Linear OA(4134, 140, F4, 96) (dual of [140, 6, 97]-code) | [i] | ||
| 3 | Linear OA(4133, 138, F4, 96) (dual of [138, 5, 97]-code) | [i] | ||
| 4 | Linear OA(2138, 150, F2, 65) (dual of [150, 12, 66]-code) | [i] | Concatenation of Two Codes | |
| 5 | Linear OA(2137, 147, F2, 65) (dual of [147, 10, 66]-code) | [i] | ||
| 6 | Linear OOA(2188, 100, F2, 2, 98) (dual of [(100, 2), 12, 99]-NRT-code) | [i] | Concatenation of Two NRT-Codes | |
| 7 | Linear OOA(444, 25, F4, 2, 32) (dual of [(25, 2), 6, 33]-NRT-code) | [i] | OOA Folding | |