Information on Result #701031
Linear OA(449, 84, F4, 22) (dual of [84, 35, 23]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,47}), C2 = C([0,15]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,47}) based on
- linear OA(431, 63, F4, 14) (dual of [63, 32, 15]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,47}, and minimum distance d ≥ |{−1,0,…,12}|+1 = 15 (BCH-bound) [i]
- linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(440, 63, F4, 22) (dual of [63, 23, 23]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,47}, and minimum distance d ≥ |{−1,0,…,20}|+1 = 23 (BCH-bound) [i]
- linear OA(428, 63, F4, 13) (dual of [63, 35, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 14 [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(49, 18, F4, 7) (dual of [18, 9, 8]-code), using
- construction X applied to C({0,1,3}) ⊂ C({1,3}) [i] based on
- linear OA(49, 17, F4, 7) (dual of [17, 8, 8]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {0,1,3}, and minimum distance d ≥ |{1,5}| + |{−6,−5,…,0}∖{−3}| = 8 (general Roos-bound) [i]
- linear OA(48, 17, F4, 6) (dual of [17, 9, 7]-code), using the cyclic code C(A) with length 17 | 44−1, defining set A = {1,3}, and minimum distance d ≥ |{−5,−3,−1,…,5}|+1 = 7 (BCH-bound) [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 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 (see above)
- construction X applied to C({0,1,3}) ⊂ C({1,3}) [i] based on
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 OOA(449, 42, F4, 2, 22) (dual of [(42, 2), 35, 23]-NRT-code) | [i] | OOA Folding | |