Information on Result #692448
Linear OA(16128, 4167, F16, 37) (dual of [4167, 4039, 38]-code), using construction X applied to Ce(36) ⊂ Ce(19) based on
- linear OA(16103, 4096, F16, 37) (dual of [4096, 3993, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(1655, 4096, F16, 20) (dual of [4096, 4041, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1625, 71, F16, 16) (dual of [71, 46, 17]-code), using
- construction X applied to AG(F,47P) ⊂ AG(F,51P) [i] based on
- linear OA(1622, 64, F16, 16) (dual of [64, 42, 17]-code), using algebraic-geometric code AG(F,47P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1618, 64, F16, 12) (dual of [64, 46, 13]-code), using algebraic-geometric code AG(F,51P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(163, 7, F16, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- linear OA(1622, 64, F16, 16) (dual of [64, 42, 17]-code), using algebraic-geometric code AG(F,47P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,47P) ⊂ AG(F,51P) [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.