MinT - Information on Result #1821563

Information on Result #1821563

OA(128⁷⁸, 65802, S₁₂₈, 27), using discarding parts of the base based on linear OA(256⁶⁸, 65802, F₂₅₆, 27) (dual of [65802, 65734, 28]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(256¹⁴, 260, F₂₅₆, 13) (dual of [260, 246, 14]-code), using
  - constructionÂ X applied to AG(F, Q+120P) âŠ‚ AG(F, Q+121P) [i] based on
    1. linear OA(256¹³, 257, F₂₅₆, 13) (dual of [257, 244, 14]-code or 257-arc in PG(12,256)), using algebraic-geometric code AG(F, Q+120P) with degQ = 3 and 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]
    2. linear OA(256¹¹, 257, F₂₅₆, 11) (dual of [257, 246, 12]-code or 257-arc in PG(10,256)), using algebraic-geometric code AG(F, Q+121P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
    3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 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]
2. linear OA(256⁵⁴, 65542, F₂₅₆, 27) (dual of [65542, 65488, 28]-code), using
  - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(256⁵³, 65537, F₂₅₆, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
    2. linear OA(256⁴⁹, 65537, F₂₅₆, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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 (see above)

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(128⁷⁸, 32901, S₁₂₈, 2, 27)	[i]		OOA Folding
2	OOA(128⁷⁸, 21934, S₁₂₈, 3, 27)	[i]		OOA Folding