Information on Result #977957
Linear OOA(768, 26, F7, 3, 45) (dual of [(26, 3), 10, 46]-NRT-code), using OOA 3-folding based on linear OA(768, 78, F7, 45) (dual of [78, 10, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(768, 79, F7, 45) (dual of [79, 11, 46]-code), using
- construction XX applied to C1 = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}), C2 = C([0,27]), C3 = C1 + C2 = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}), 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}) [i] 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 = {1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}, and minimum distance d ≥ |{−3,2,7,…,−5}|+1 = 40 (BCH-bound) [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(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(737, 48, F7, 26) (dual of [48, 11, 27]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}, and minimum distance d ≥ |{6,7,…,31}|+1 = 27 (BCH-bound) [i]
- linear OA(716, 23, F7, 12) (dual of [23, 7, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(716, 32, F7, 12) (dual of [32, 16, 13]-code), using
- extended quadratic residue code Qe(32,7) [i]
- discarding factors / shortening the dual code based on linear OA(716, 32, F7, 12) (dual of [32, 16, 13]-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]
- construction XX applied to C1 = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}), C2 = C([0,27]), C3 = C1 + C2 = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}), 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}) [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.