MinT - Information on Result #1832206

Information on Result #1832206

OOA(32⁹⁷, 1048621, S₃₂, 2, 21), 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]
OOA(32⁸⁶, 1048577, S₃₂, 2, 21), using
- OOA 2-folding [i] based on OA(32⁸⁶, 2097154, S₃₂, 21), using
  - discarding factors based on OA(32⁸⁶, 2097155, S₃₂, 21), using
    - discarding parts of the base [i] based on linear OA(128⁶¹, 2097155, F₁₂₈, 21) (dual of [2097155, 2097094, 22]-code), using
      - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
        linear OA(128⁶¹, 2097152, F₁₂₈, 21) (dual of [2097152, 2097091, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(128⁵⁸, 2097152, F₁₂₈, 20) (dual of [2097152, 2097094, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
        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.

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	OOA(32⁹⁷, 209724, S₃₂, 22, 21)	[i]		OOA Folding and Stacking with Additional Row