MinT - Information on Result #681665

Information on Result #681665

Linear OA(4¹⁴², 290, F₄, 46) (dual of [290, 148, 47]-code), using constructionÂ X applied to C_e(45) âŠ‚ C_e(37) based on

linear OA(4¹²⁹, 256, F₄, 46) (dual of [256, 127, 47]-code), using an extension C_e(45) of the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,45], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 46 [i]
linear OA(4¹⁰⁵, 256, F₄, 38) (dual of [256, 151, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
linear OA(4¹³, 34, F₄, 7) (dual of [34, 21, 8]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
    - ovoid in PG(3,Â 4) [i]
  2. linear OA(4⁹, 17, F₄, 7) (dual of [17, 8, 8]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(4⁸, 17, F₄, 6) (dual of [17, 9, 7]-code), using
        the BCH-code C(I) with length 17Â | 4⁴âˆ’1, defining interval IÂ =Â {1,4,7,…,16}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. nonexistence of linear OA(4⁷, 10, F₄, 6) (dual of [10, 3, 7]-code), because
        bound for almost-MDS-codes with dimension nÂ =Â 3 [i]

Mode: Constructive and linear.

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