Information on Result #701440
Linear OA(752, 76, F7, 28) (dual of [76, 24, 29]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,20,27,34,40,41}), C2 = C([1,19]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,27,34,40,41}) based on
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,20,27,34,40,41}, and minimum distance d ≥ |{−8,−7,…,16}|+1 = 26 (BCH-bound) [i]
- linear OA(730, 48, F7, 19) (dual of [48, 18, 20]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,27,34,40,41}, and minimum distance d ≥ |{−8,−7,…,23}|+1 = 33 (BCH-bound) [i]
- linear OA(724, 48, F7, 16) (dual of [48, 24, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [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(752, 38, F7, 2, 28) (dual of [(38, 2), 24, 29]-NRT-code) | [i] | OOA Folding | |