MinT - Information on Result #898453

Information on Result #898453

Linear OOA(16¹⁰², 524358, F₁₆, 2, 19) (dual of [(524358, 2), 1048614, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16¹⁵, 65, F₁₆, 2, 9) (dual of [(65, 2), 115, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,120P) [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(16⁸⁷, 524293, F₁₆, 2, 19) (dual of [(524293, 2), 1048499, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁸⁷, 1048586, F₁₆, 19) (dual of [1048586, 1048499, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁸⁷, 1048587, F₁₆, 19) (dual of [1048587, 1048500, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(16) [i] based on
      1. linear OA(16⁸⁶, 1048576, F₁₆, 19) (dual of [1048576, 1048490, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.