Information on Result #1303687
Linear OA(1667, 4118, F16, 22) (dual of [4118, 4051, 23]-code), using construction X with Varšamov bound based on
- linear OA(1666, 4116, F16, 22) (dual of [4116, 4050, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(1661, 4096, F16, 22) (dual of [4096, 4035, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1646, 4096, F16, 17) (dual of [4096, 4050, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(165, 20, F16, 4) (dual of [20, 15, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(165, 24, F16, 4) (dual of [24, 19, 5]-code), using
- extended algebraic-geometric code AGe(F,19P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(165, 24, F16, 4) (dual of [24, 19, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(1666, 4117, F16, 21) (dual of [4117, 4051, 22]-code), using Gilbert–Varšamov bound and bm = 1666 > Vbs−1(k−1) = 254255 234318 368033 423987 508733 988896 736747 893288 485876 443821 398982 684831 855616 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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.