MinT - Information on Result #1013202

Information on Result #1013202

Linear OOA(5⁶⁹, 5224, F₅, 3, 13) (dual of [(5224, 3), 15603, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5⁸, 14, F₅, 3, 6) (dual of [(14, 3), 34, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 8, 14)-net over F₅, using
  - linear code embedding found in a computer search [i]
linear OOA(5⁶¹, 5210, F₅, 3, 13) (dual of [(5210, 3), 15569, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁶¹, 15630, F₅, 13) (dual of [15630, 15569, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁶¹, 15631, F₅, 13) (dual of [15631, 15570, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(5⁶¹, 15625, F₅, 13) (dual of [15625, 15564, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(5⁵⁵, 15625, F₅, 12) (dual of [15625, 15570, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(5⁰, 6, F₅, 0) (dual of [6, 6, 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: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5⁶⁹, 2611, F₅, 15, 13) (dual of [(2611, 15), 39096, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row