Information on Result #681974
Linear OA(461, 69, F4, 44) (dual of [69, 8, 45]-code), using construction XX applied to C([1,140]) ⊂ C([1,128]) ⊂ C([1,125]) based on
- 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(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(455, 63, F4, 41) (dual of [63, 8, 42]-code), using contraction [i] based on linear OA(4181, 189, F4, 125) (dual of [189, 8, 126]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,125], and designed minimum distance d ≥ |I|+1 = 126 [i]
- linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(461, 69, F4, 43) (dual of [69, 8, 44]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(461, 69, F4, 42) (dual of [69, 8, 43]-code) | [i] | ||
| 3 | Linear OA(461, 69, F4, 41) (dual of [69, 8, 42]-code) | [i] | ||
| 4 | Linear OA(461, 69, F4, 40) (dual of [69, 8, 41]-code) | [i] | ||
| 5 | Linear OA(2191, 207, F2, 89) (dual of [207, 16, 90]-code) | [i] | Concatenation of Two Codes | |
| 6 | Linear OOA(2260, 138, F2, 2, 134) (dual of [(138, 2), 16, 135]-NRT-code) | [i] | Concatenation of Two NRT-Codes | |
| 7 | Linear OOA(461, 23, F4, 3, 44) (dual of [(23, 3), 8, 45]-NRT-code) | [i] | OOA Folding | |