MinT - Information on Result #685877

Information on Result #685877

Linear OA(7⁵⁰, 59, F₇, 37) (dual of [59, 9, 38]-code), using constructionÂ X applied to C([1,79]) âŠ‚ C([1,63]) based on

linear OA(7⁴⁴, 48, F₇, 39) (dual of [48, 4, 40]-code), using contraction [i] based on linear OA(7⁹², 96, F₇, 79) (dual of [96, 4, 80]-code), using the narrow-sense BCH-code C(I) with length 96Â | 7⁴âˆ’1, defining interval IÂ =Â [1,79], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 80 [i]
linear OA(7³⁹, 48, F₇, 31) (dual of [48, 9, 32]-code), using contraction [i] based on linear OA(7⁸⁷, 96, F₇, 63) (dual of [96, 9, 64]-code), using the narrow-sense BCH-code C(I) with length 96Â | 7⁴âˆ’1, defining interval IÂ =Â [1,63], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 64 [i]
linear OA(7⁶, 11, F₇, 5) (dual of [11, 5, 6]-code), using
- construction for [s,Â sâˆ’6,Â 6]-code from [s,Â 3,Â sâˆ’3]-code [i] based on linear OA(7⁸, 11, F₇, 7) (dual of [11, 3, 8]-code), using
  - constructionÂ X applied to C₁ âŠ‚ C₀ [i] based on
    1. linear OA(7⁷, 8, F₇, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using code C₁ for uÂ =Â 2 by de Boer and Brouwer [i]
    2. linear OA(7⁵, 8, F₇, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using code C₀ for uÂ =Â 2 by de Boer and Brouwer [i]
    3. linear OA(7¹, 3, F₇, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(7⁵⁰, 59, F₇, 36) (dual of [59, 9, 37]-code)	[i]		Strength Reduction
2	Linear OA(7⁵⁰, 59, F₇, 35) (dual of [59, 9, 36]-code)	[i]		Strength Reduction