Information on Result #701531
Linear OA(762, 72, F7, 42) (dual of [72, 10, 43]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,33,34,41}), C2 = C([0,32]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}) based on
- linear OA(744, 48, F7, 39) (dual of [48, 4, 40]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,33,34,41}, and minimum distance d ≥ |{−11,−6,−1,…,−13}|+1 = 40 (BCH-bound) [i]
- linear OA(741, 48, F7, 33) (dual of [48, 7, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(747, 48, F7, 47) (dual of [48, 1, 48]-code or 48-arc in PG(46,7)), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}, and minimum distance d ≥ |{3,14,25,…,−19}|+1 = 48 (BCH-bound) [i]
- linear OA(738, 48, F7, 27) (dual of [48, 10, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(710, 16, F7, 8) (dual of [16, 6, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- discarding factors / shortening the dual code based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using
- extended Reed–Solomon code RSe(3,7) [i]
- the expurgated narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
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(762, 36, F7, 2, 42) (dual of [(36, 2), 10, 43]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(762, 24, F7, 3, 42) (dual of [(24, 3), 10, 43]-NRT-code) | [i] | ||