Information on Result #701040
Linear OA(449, 78, F4, 23) (dual of [78, 29, 24]-code), using construction XX applied to C1 = C({1,2,3,5,7,9,10,11,13,14,15,21,22}), C2 = C([0,21]), C3 = C1 + C2 = C({1,2,3,5,7,9,10,11,13,14,15,21}), and C∩ = C1 ∩ C2 = C([0,22]) based on
- linear OA(437, 63, F4, 16) (dual of [63, 26, 17]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {1,2,3,5,7,9,10,11,13,14,15,21,22}, and minimum distance d ≥ |{7,8,…,22}|+1 = 17 (BCH-bound) [i]
- linear OA(438, 63, F4, 22) (dual of [63, 25, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(434, 63, F4, 15) (dual of [63, 29, 16]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {1,2,3,5,7,9,10,11,13,14,15,21}, and minimum distance d ≥ |{7,8,…,21}|+1 = 16 (BCH-bound) [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(48, 12, F4, 6) (dual of [12, 4, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 16, F4, 6) (dual of [16, 8, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15 = 42−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(48, 16, F4, 6) (dual of [16, 8, 7]-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.
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Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(449, 39, F4, 2, 23) (dual of [(39, 2), 29, 24]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(449, 26, F4, 3, 23) (dual of [(26, 3), 29, 24]-NRT-code) | [i] | ||