MinT - Information on Result #1831666

Information on Result #1831666

OOA(16⁷², 1048601, S₁₆, 2, 13), using (u,Â u+v)-construction based on

linear OOA(16⁷, 24, F₁₆, 2, 6) (dual of [(24, 2), 41, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,41P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
  - a function field by SÃ©mirat [i]
OOA(16⁶⁵, 1048577, S₁₆, 2, 13), using
- OOA 2-folding [i] based on OA(16⁶⁵, 2097154, S₁₆, 13), using
  - discarding factors based on OA(16⁶⁵, 2097155, S₁₆, 13), using
    - discarding parts of the base [i] based on linear OA(128³⁷, 2097155, F₁₂₈, 13) (dual of [2097155, 2097118, 14]-code), using
      - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(128³⁷, 2097152, F₁₂₈, 13) (dual of [2097152, 2097115, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(128³⁴, 2097152, F₁₂₈, 12) (dual of [2097152, 2097118, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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(16⁷², 349533, S₁₆, 14, 13)	[i]		OOA Folding and Stacking with Additional Row