Information on Result #701481
Linear OA(746, 63, F7, 28) (dual of [63, 17, 29]-code), using construction XX applied to C1 = C({1,2,3,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}), C2 = C([0,24]), C3 = C1 + C2 = C({1,2,3,5,6,8,9,10,11,12,13,16,17,18,19,20,24}), and C∩ = C1 ∩ C2 = C([0,27]) based on
- linear OA(737, 48, F7, 23) (dual of [48, 11, 24]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}, and minimum distance d ≥ |{5,6,…,27}|+1 = 24 (BCH-bound) [i]
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(731, 48, F7, 20) (dual of [48, 17, 21]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,5,6,8,9,10,11,12,13,16,17,18,19,20,24}, and minimum distance d ≥ |{5,6,…,24}|+1 = 21 (BCH-bound) [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]
- linear OA(74, 7, F7, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), using
- Reed–Solomon code RS(3,7) [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.
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Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(746, 21, F7, 3, 28) (dual of [(21, 3), 17, 29]-NRT-code) | [i] | OOA Folding | |