MinT - Information on Result #898562

Information on Result #898562

Linear OOA(16¹²⁴, 524358, F₁₆, 2, 23) (dual of [(524358, 2), 1048592, 24]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16¹⁷, 65, F₁₆, 2, 11) (dual of [(65, 2), 113, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,118P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]
linear OOA(16¹⁰⁷, 524293, F₁₆, 2, 23) (dual of [(524293, 2), 1048479, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16¹⁰⁷, 1048586, F₁₆, 23) (dual of [1048586, 1048479, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁰⁷, 1048587, F₁₆, 23) (dual of [1048587, 1048480, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
      1. linear OA(16¹⁰⁶, 1048576, F₁₆, 23) (dual of [1048576, 1048470, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(16⁹⁶, 1048576, F₁₆, 21) (dual of [1048576, 1048480, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(16¹, 11, F₁₆, 1) (dual of [11, 10, 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]

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

None.