MinT - Information on Result #1821259

Information on Result #1821259

OA(128⁴⁸, 65799, S₁₂₈, 17), using discarding parts of the base based on linear OA(256⁴², 65799, F₂₅₆, 17) (dual of [65799, 65757, 18]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256⁸, 257, F₂₅₆, 8) (dual of [257, 249, 9]-code or 257-arc in PG(7,256)), using
  - extended Reedâ€“Solomon code RS_e(249,256) [i]
  - algebraic-geometric code AG(F,124P) with degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
  - algebraic-geometric code AG(F, Q+82P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  - algebraic-geometric code AG(F, Q+49P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
2. linear OA(256³⁴, 65542, F₂₅₆, 17) (dual of [65542, 65508, 18]-code), using
  - constructionÂ X applied to C([0,8]) âŠ‚ C([0,7]) [i] based on
    1. linear OA(256³³, 65537, F₂₅₆, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    2. linear OA(256²⁹, 65537, F₂₅₆, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(128⁴⁸, 32899, S₁₂₈, 2, 17)	[i]		OOA Folding
2	OOA(128⁴⁸, 21933, S₁₂₈, 3, 17)	[i]		OOA Folding