MinT - Information on Result #902669

Information on Result #902669

Linear OOA(32⁹⁴, 634, F₃₂, 2, 34) (dual of [(634, 2), 1174, 35]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32²⁸, 120, F₃₂, 2, 17) (dual of [(120, 2), 212, 18]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,222P) [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
  - a function field by SÃ©mirat [i]
linear OOA(32⁶⁶, 514, F₃₂, 2, 34) (dual of [(514, 2), 962, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁶⁶, 1028, F₃₂, 34) (dual of [1028, 962, 35]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁶⁶, 1029, F₃₂, 34) (dual of [1029, 963, 35]-code), using
    - constructionÂ X applied to C_e(33) âŠ‚ C_e(30) [i] based on
      1. linear OA(32⁶⁴, 1024, F₃₂, 34) (dual of [1024, 960, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      2. linear OA(32⁶¹, 1024, F₃₂, 31) (dual of [1024, 963, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      3. linear OA(32², 5, F₃₂, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,32)), using
        discarding factors / shortening the dual code based on linear OA(32², 32, F₃₂, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
        Reedâ€“Solomon code RS(30,32) [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

None.