MinT - Information on Result #735698

Information on Result #735698

Linear OA(128⁶⁹, 2097434, F₁₂₈, 19) (dual of [2097434, 2097365, 20]-code), using (u,Â u+v)-construction based on

linear OA(128¹⁴, 279, F₁₂₈, 9) (dual of [279, 265, 10]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(128⁴, 129, F₁₂₈, 4) (dual of [129, 125, 5]-code or 129-arc in PG(3,128)), using
    - extended Reedâ€“Solomon code RS_e(125,128) [i]
  2. linear OA(128¹⁰, 150, F₁₂₈, 9) (dual of [150, 140, 10]-code), using
    - extended algebraic-geometric code AG_e(F,140P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]
linear OA(128⁵⁵, 2097155, F₁₂₈, 19) (dual of [2097155, 2097100, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
  1. linear OA(128⁵⁵, 2097152, F₁₂₈, 19) (dual of [2097152, 2097097, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. linear OA(128⁵², 2097152, F₁₂₈, 18) (dual of [2097152, 2097100, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
  3. linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(128⁶⁹, 1048717, F₁₂₈, 2, 19) (dual of [(1048717, 2), 2097365, 20]-NRT-code)	[i]		OOA Folding