MinT - Information on Result #2211358

Information on Result #2211358

Linear OA(5¹⁵⁰, 204, F₅, 72) (dual of [204, 54, 73]-code), using strength reduction based on linear OA(5¹⁵⁰, 204, F₅, 73) (dual of [204, 54, 74]-code), using

concatenation of two codes [i] based on
1. linear OA(25⁴¹, 68, F₂₅, 36) (dual of [68, 27, 37]-code), using
  - constructionÂ X applied to AG(F,28P) âŠ‚ AG(F,30P) [i] based on
    1. linear OA(25⁴⁰, 65, F₂₅, 36) (dual of [65, 25, 37]-code), using algebraic-geometric code AG(F,28P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]
    2. linear OA(25³⁸, 65, F₂₅, 34) (dual of [65, 27, 35]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹⁵⁰, 102, F₅, 2, 72) (dual of [(102, 2), 54, 73]-NRT-code)	[i]		OOA Folding
2	Linear OOA(5¹⁵⁰, 68, F₅, 3, 72) (dual of [(68, 3), 54, 73]-NRT-code)	[i]		OOA Folding