MinT - Information on Result #898766

Information on Result #898766

Linear OOA(16¹⁰⁸, 2118, F₁₆, 2, 30) (dual of [(2118, 2), 4128, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16²¹, 65, F₁₆, 2, 15) (dual of [(65, 2), 109, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,114P) [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, 2053, F₁₆, 2, 30) (dual of [(2053, 2), 4019, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁸⁷, 4106, F₁₆, 30) (dual of [4106, 4019, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁸⁷, 4107, F₁₆, 30) (dual of [4107, 4020, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(26) [i] based on
      1. linear OA(16⁸⁵, 4096, F₁₆, 30) (dual of [4096, 4011, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(16⁷⁶, 4096, F₁₆, 27) (dual of [4096, 4020, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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.