MinT - Information on Result #1488908

Information on Result #1488908

Linear OOA(8³⁹, 1923, F₈, 3, 11) (dual of [(1923, 3), 5730, 12]-NRT-code), using OOA 2-folding based on linear OOA(8³⁹, 3846, F₈, 2, 11) (dual of [(3846, 2), 7653, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8³⁹, 3847, F₈, 2, 11) (dual of [(3847, 2), 7655, 12]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8³⁹, 3847, F₈, 11) (dual of [3847, 3808, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(8³⁹, 4106, F₈, 11) (dual of [4106, 4067, 12]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(8³⁸, 4105, F₈, 11) (dual of [4105, 4067, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(8) [i] based on
        linear OA(8³⁷, 4096, F₈, 11) (dual of [4096, 4059, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(8²⁹, 4096, F₈, 9) (dual of [4096, 4067, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(8¹, 9, F₈, 1) (dual of [9, 8, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.