MinT - Information on Result #898822

Information on Result #898822

Linear OOA(16¹¹³, 2114, F₁₆, 2, 32) (dual of [(2114, 2), 4115, 33]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16²², 65, F₁₆, 2, 16) (dual of [(65, 2), 108, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,113P) [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(16⁹¹, 2049, F₁₆, 2, 32) (dual of [(2049, 2), 4007, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁹¹, 4098, F₁₆, 32) (dual of [4098, 4007, 33]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁹¹, 4099, F₁₆, 32) (dual of [4099, 4008, 33]-code), using
    - 1 times truncation [i] based on linear OA(16⁹², 4100, F₁₆, 33) (dual of [4100, 4008, 34]-code), using
      - constructionÂ X applied to C_e(32) âŠ‚ C_e(30) [i] based on
        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]
        linear OA(16⁸⁸, 4096, F₁₆, 31) (dual of [4096, 4008, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(16¹, 4, F₁₆, 1) (dual of [4, 3, 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.