MinT - Information on Result #1724119

Information on Result #1724119

Linear OOA(5¹¹⁷, 744, F₅, 33, 27) (dual of [(744, 33), 24435, 28]-NRT-code), using OOA 5-folding and stacking with additional row based on linear OOA(5¹¹⁷, 3721, F₅, 3, 27) (dual of [(3721, 3), 11046, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(5¹¹⁷, 3722, F₅, 3, 27) (dual of [(3722, 3), 11049, 28]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹¹⁷, 3722, F₅, 27) (dual of [3722, 3605, 28]-code), using
  - 581 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 18 times 0, 1, 37 times 0, 1, 66 times 0, 1, 104 times 0, 1, 147 times 0, 1, 188 times 0) [i] based on linear OA(5¹⁰⁶, 3130, F₅, 27) (dual of [3130, 3024, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
      1. linear OA(5¹⁰⁶, 3125, F₅, 27) (dual of [3125, 3019, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(5¹⁰¹, 3125, F₅, 26) (dual of [3125, 3024, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (90, 117, 744)-net over F₅	[i]		Net Defined by OOA