MinT - Information on Result #898921

Information on Result #898921

Linear OOA(16¹²⁷, 2119, F₁₆, 2, 36) (dual of [(2119, 2), 4111, 37]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16²⁴, 65, F₁₆, 2, 18) (dual of [(65, 2), 106, 19]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,111P) [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(16¹⁰³, 2054, F₁₆, 2, 36) (dual of [(2054, 2), 4005, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16¹⁰³, 4108, F₁₆, 36) (dual of [4108, 4005, 37]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(16¹⁰², 4107, F₁₆, 36) (dual of [4107, 4005, 37]-code), using
    - constructionÂ X applied to C_e(35) âŠ‚ C_e(32) [i] based on
      1. linear OA(16¹⁰⁰, 4096, F₁₆, 36) (dual of [4096, 3996, 37]-code), using an extension C_e(35) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,35], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
      2. linear OA(16⁹¹, 4096, F₁₆, 33) (dual of [4096, 4005, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      3. linear OA(16², 11, F₁₆, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,16)), using
        discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
        Reedâ€“Solomon code RS(14,16) [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.