Information on Result #823968
Linear OOA(444, 34, F4, 2, 24) (dual of [(34, 2), 24, 25]-NRT-code), using OOA 2-folding based on linear OA(444, 68, F4, 24) (dual of [68, 24, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(444, 69, F4, 24) (dual of [69, 25, 25]-code), using
- construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,47}), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,47}) [i] based on
- linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,47}, and minimum distance d ≥ |{−1,0,…,21}|+1 = 24 (BCH-bound) [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(444, 63, F4, 24) (dual of [63, 19, 25]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,47}, and minimum distance d ≥ |{−1,0,…,22}|+1 = 25 (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(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(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,47}), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,47}) [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.
Other Results with Identical Parameters
None.
Depending Results
None.