MinT - Information on Result #2261810

Information on Result #2261810

Linear OA(2²⁴⁰, 336, F₂, 72) (dual of [336, 96, 73]-code), using 2 times code embedding in larger space based on linear OA(2²³⁸, 334, F₂, 72) (dual of [334, 96, 73]-code), using

1 times truncation [i] based on linear OA(2²³⁹, 335, F₂, 73) (dual of [335, 96, 74]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16⁴³, 67, F₁₆, 36) (dual of [67, 24, 37]-code), using
    - constructionÂ X applied to AG(F,27P) âŠ‚ AG(F,29P) [i] based on
      1. linear OA(16⁴², 64, F₁₆, 36) (dual of [64, 22, 37]-code), using algebraic-geometric code AG(F,27P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]
      2. linear OA(16⁴⁰, 64, F₁₆, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
      3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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(2²⁴⁰, 112, F₂, 3, 72) (dual of [(112, 3), 96, 73]-NRT-code)	[i]		OOA Folding