MinT - Information on Result #1589401

Information on Result #1589401

Linear OOA(2⁷⁹, 2715, F₂, 4, 12) (dual of [(2715, 4), 10781, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁷⁹, 2715, F₂, 3, 12) (dual of [(2715, 3), 8066, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁷⁹, 2735, F₂, 3, 12) (dual of [(2735, 3), 8126, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁷⁹, 8205, F₂, 12) (dual of [8205, 8126, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁷⁹, 8206, F₂, 12) (dual of [8206, 8127, 13]-code), using
    - 1 times truncation [i] based on linear OA(2⁸⁰, 8207, F₂, 13) (dual of [8207, 8127, 14]-code), using
      - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
        linear OA(2⁷⁹, 8192, F₂, 13) (dual of [8192, 8113, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(2⁶⁶, 8192, F₂, 11) (dual of [8192, 8126, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2¹⁴, 15, F₂, 13) (dual of [15, 1, 14]-code), using
        strength reduction [i] based on linear OA(2¹⁴, 15, F₂, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
        dual of repetition code with length 15 [i]
        linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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.