Information on Result #701110
Linear OA(468, 75, F4, 50) (dual of [75, 7, 51]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,47}), C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43}), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43,47}) based on
- linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,47}, and minimum distance d ≥ |{−4,−3,…,41}|+1 = 47 (BCH-bound) [i]
- linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43}, and minimum distance d ≥ |{1,6,11,…,−26}|+1 = 47 (BCH-bound) [i]
- linear OA(462, 63, F4, 62) (dual of [63, 1, 63]-code or 63-arc in PG(61,4)), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43,47}, and minimum distance d ≥ |{1,23,45,…,20}|+1 = 63 (BCH-bound) [i]
- linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
- linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)) (see above)
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(468, 75, F4, 49) (dual of [75, 7, 50]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(467, 74, F4, 49) (dual of [74, 7, 50]-code) | [i] | Truncation | |
| 3 | Linear OA(466, 73, F4, 48) (dual of [73, 7, 49]-code) | [i] | ||
| 4 | Linear OA(4141, 146, F4, 101) (dual of [146, 5, 102]-code) | [i] | Repeating Each Code Word | |
| 5 | Linear OA(4143, 150, F4, 101) (dual of [150, 7, 102]-code) | [i] | ||
| 6 | Linear OA(4157, 162, F4, 114) (dual of [162, 5, 115]-code) | [i] | Juxtaposition | |
| 7 | Linear OA(4136, 143, F4, 96) (dual of [143, 7, 97]-code) | [i] | ||
| 8 | Linear OA(4137, 144, F4, 97) (dual of [144, 7, 98]-code) | [i] | ||
| 9 | Linear OA(4138, 145, F4, 98) (dual of [145, 7, 99]-code) | [i] | ||
| 10 | Linear OA(2210, 222, F2, 101) (dual of [222, 12, 102]-code) | [i] | Concatenation of Two Codes | |
| 11 | Linear OA(2209, 219, F2, 101) (dual of [219, 10, 102]-code) | [i] | ||
| 12 | Linear OA(2211, 225, F2, 101) (dual of [225, 14, 102]-code) | [i] | ||
| 13 | Linear OOA(468, 37, F4, 2, 50) (dual of [(37, 2), 6, 51]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(468, 25, F4, 3, 50) (dual of [(25, 3), 7, 51]-NRT-code) | [i] | ||