MinT - Information on Result #902248

Information on Result #902248

Linear OOA(32⁶⁹, 16429, F₃₂, 2, 20) (dual of [(16429, 2), 32789, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹¹, 44, F₃₂, 2, 10) (dual of [(44, 2), 77, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,77P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
  - a function field by SÃ©mirat [i]
linear OOA(32⁵⁸, 16385, F₃₂, 2, 20) (dual of [(16385, 2), 32712, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁵⁸, 32770, F₃₂, 20) (dual of [32770, 32712, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁵⁸, 32771, F₃₂, 20) (dual of [32771, 32713, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
      1. linear OA(32⁵⁸, 32768, F₃₂, 20) (dual of [32768, 32710, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(32⁵⁵, 32768, F₃₂, 19) (dual of [32768, 32713, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(32⁰, 3, F₃₂, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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(32⁶⁹, 3285, F₃₂, 22, 20) (dual of [(3285, 22), 72201, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row