MinT - Information on Result #2245894

Information on Result #2245894

Linear OA(5⁶⁴, 86, F₅, 34) (dual of [86, 22, 35]-code), using 1 times truncation based on linear OA(5⁶⁵, 87, F₅, 35) (dual of [87, 22, 36]-code), using

concatenation of two codes [i] based on
1. linear OA(25¹⁸, 29, F₂₅, 17) (dual of [29, 11, 18]-code), using
  - constructionÂ X applied to AG(F,4P) âŠ‚ AG(F,5P) [i] based on
    1. linear OA(25¹⁷, 26, F₂₅, 17) (dual of [26, 9, 18]-code or 26-arc in PG(16,25)), using algebraic-geometric code AG(F,4P) with degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
    2. linear OA(25¹⁵, 26, F₂₅, 15) (dual of [26, 11, 16]-code or 26-arc in PG(14,25)), using algebraic-geometric code AG(F,5P) with degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
    3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(5¹, 3, F₅, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5⁶⁴, 43, F₅, 2, 34) (dual of [(43, 2), 22, 35]-NRT-code)	[i]		OOA Folding