MinT - Information on Result #1441076

Information on Result #1441076

Linear OOA(7⁵¹, 612603, F₇, 2, 9) (dual of [(612603, 2), 1225155, 10]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(7⁵¹, 612603, F₇, 9) (dual of [612603, 612552, 10]-code), using

discarding factors / shortening the dual code based on linear OA(7⁵¹, 823552, F₇, 9) (dual of [823552, 823501, 10]-code), using
- constructionÂ X4 applied to C([0,8]) âŠ‚ C([1,7]) [i] based on
  1. linear OA(7⁵⁰, 823542, F₇, 9) (dual of [823542, 823492, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [0,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
  2. linear OA(7⁴², 823542, F₇, 7) (dual of [823542, 823500, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
  3. linear OA(7⁹, 10, F₇, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,7)), using
    - dual of repetition code with length 10 [i]
  4. linear OA(7¹, 10, F₇, 1) (dual of [10, 9, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(7¹, 342, F₇, 1) (dual of [342, 341, 2]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 342Â = 7³âˆ’1, defining interval IÂ =Â [0,0], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁵¹, 306301, F₇, 3, 9) (dual of [(306301, 3), 918852, 10]-NRT-code)	[i]		OOA Folding
2	Linear OOA(7⁵¹, 306301, F₇, 10, 9) (dual of [(306301, 10), 3062959, 10]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row