MinT - Information on Result #1013889

Information on Result #1013889

Linear OOA(7⁷⁹, 274532, F₇, 3, 12) (dual of [(274532, 3), 823517, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7⁷, 13, F₇, 3, 6) (dual of [(13, 3), 32, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 7, 13)-net over F₇, using
  - 6 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
linear OOA(7⁷², 274519, F₇, 3, 12) (dual of [(274519, 3), 823485, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁷², 823557, F₇, 12) (dual of [823557, 823485, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁷², 823558, F₇, 12) (dual of [823558, 823486, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(9) [i] based on
      1. linear OA(7⁷¹, 823543, F₇, 12) (dual of [823543, 823472, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(7⁵⁷, 823543, F₇, 10) (dual of [823543, 823486, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(7¹, 15, F₇, 1) (dual of [15, 14, 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 OOA(7⁷⁹, 137265, F₇, 15, 12) (dual of [(137265, 15), 2058896, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row