MinT - Information on Result #1705141

Information on Result #1705141

Linear OOA(2²³⁷, 265170, F₂, 8, 23) (dual of [(265170, 8), 2121123, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁷, 265170, F₂, 7, 23) (dual of [(265170, 7), 1855953, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³⁷, 299597, F₂, 7, 23) (dual of [(299597, 7), 2096942, 24]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2²³⁷, 2097179, F₂, 23) (dual of [2097179, 2096942, 24]-code), using
  - 3 times code embedding in larger space [i] based on linear OA(2²³⁴, 2097176, F₂, 23) (dual of [2097176, 2096942, 24]-code), using
    - adding a parity check bit [i] based on linear OA(2²³³, 2097175, F₂, 22) (dual of [2097175, 2096942, 23]-code), using
      - constructionÂ X4 applied to C([0,22]) âŠ‚ C([1,20]) [i] based on
        linear OA(2²³², 2097151, F₂, 23) (dual of [2097151, 2096919, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]
        linear OA(2²¹⁰, 2097151, F₂, 20) (dual of [2097151, 2096941, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(2²³, 24, F₂, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
        dual of repetition code with length 24 [i]
        linear OA(2¹, 24, F₂, 1) (dual of [24, 23, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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.