Information on Result #737453
Linear OA(465, 82, F4, 35) (dual of [82, 17, 36]-code), using construction XX applied to C1 = C([0,80]), C2 = C([1,125]), C3 = C1 + C2 = C([1,80]), and C∩ = C1 ∩ C2 = C([0,125]) based on
- linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using contraction [i] based on linear OA(4173, 189, F4, 83) (dual of [189, 16, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,80], and minimum distance d ≥ |{−2,−1,…,80}|+1 = 84 (BCH-bound) [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(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 expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,125], and minimum distance d ≥ |{−2,−1,…,125}|+1 = 129 (BCH-bound) [i]
- linear OA(446, 63, F4, 26) (dual of [63, 17, 27]-code), using contraction [i] based on linear OA(4172, 189, F4, 80) (dual of [189, 17, 81]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,80], and designed minimum distance d ≥ |I|+1 = 81 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- 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, using
- 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(465, 41, F4, 2, 35) (dual of [(41, 2), 17, 36]-NRT-code) | [i] | OOA Folding | |