Information on Result #711625
Linear OA(5124, 672, F5, 34) (dual of [672, 548, 35]-code), using construction XX applied to C1 = C([125,155]), C2 = C([133,158]), C3 = C1 + C2 = C([133,155]), and C∩ = C1 ∩ C2 = C([125,158]) based on
- linear OA(598, 624, F5, 31) (dual of [624, 526, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {125,126,…,155}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(585, 624, F5, 26) (dual of [624, 539, 27]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {133,134,…,158}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(5107, 624, F5, 34) (dual of [624, 517, 35]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {125,126,…,158}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(576, 624, F5, 23) (dual of [624, 548, 24]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {133,134,…,155}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(514, 36, F5, 7) (dual of [36, 22, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-code), using
- trace code [i] based on linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- extended Reed–Solomon code RSe(19,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- algebraic-geometric code AG(F,9P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F,6P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- trace code [i] based on linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-code), using
- linear OA(53, 12, F5, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
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.