MinT - Information on Result #1624911

Information on Result #1624911

Linear OOA(256⁵⁷, 32913, F₂₅₆, 5, 23) (dual of [(32913, 5), 164508, 24]-NRT-code), using OOA 2-folding based on linear OOA(256⁵⁷, 65826, F₂₅₆, 3, 23) (dual of [(65826, 3), 197421, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁵⁷, 65827, F₂₅₆, 3, 23) (dual of [(65827, 3), 197424, 24]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(256⁵⁷, 65827, F₂₅₆, 23) (dual of [65827, 65770, 24]-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OA(256¹², 289, F₂₅₆, 11) (dual of [289, 277, 12]-code), using
      - extended algebraic-geometric code AG_e(F,277P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
        sharp bound on the number of rational points on curves with genus 1 [i]
    2. linear OA(256⁴⁵, 65538, F₂₅₆, 23) (dual of [65538, 65493, 24]-code), using
      - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
        linear OA(256⁴⁵, 65536, F₂₅₆, 23) (dual of [65536, 65491, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(256⁴³, 65536, F₂₅₆, 22) (dual of [65536, 65493, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: 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.