MinT - Information on Result #1485875

Information on Result #1485875

Linear OOA(5¹²⁴, 1775, F₅, 3, 29) (dual of [(1775, 3), 5201, 30]-NRT-code), using OOA 2-folding based on linear OOA(5¹²⁴, 3550, F₅, 2, 29) (dual of [(3550, 2), 6976, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(5¹²⁴, 3551, F₅, 2, 29) (dual of [(3551, 2), 6978, 30]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹²⁴, 3551, F₅, 29) (dual of [3551, 3427, 30]-code), using
  - 413 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 0, 0, 1, 6 times 0, 1, 16 times 0, 1, 36 times 0, 1, 69 times 0, 1, 116 times 0, 1, 161 times 0) [i] based on linear OA(5¹¹⁶, 3130, F₅, 29) (dual of [3130, 3014, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
      1. linear OA(5¹¹⁶, 3125, F₅, 29) (dual of [3125, 3009, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(5¹¹¹, 3125, F₅, 28) (dual of [3125, 3014, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(5⁰, 5, F₅, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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.