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Syarifatul Azaliyah, Syarifatul
brawijaya university
Computer Science & IT Education Mathematics Other

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Ring of Weight Enumerator of Integer Azaliyah, Syarifatul; Hamid, Nur; Alghofari, Abdul Rouf; Anam, Syaiful
Indonesian Journal of Mathematics and Applications Vol. 2 No. 2 (2024): Indonesian Journal of Mathematics and Applications (IJMA)
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2024.002.02.3

Abstract

 Invariant theory can be combined with coding theory to analyze the polynomial ring over its weight enumerator. For a certain class code, especially for self-dual doubly even code or type II code, the polynomials over its code satisfy the invarian condition. In this paper, we will  show that the ring of the weight enumerator over integer of self-dual doubly even code $d_{48}^+$ cannot be ganerated by the weight enumerator of self-dual doubly even code with code length n=8, 16, 24, 32 and 40. 
Ring of Weight Enumerator of Integer Azaliyah, Syarifatul; Hamid, Nur; Alghofari, Abdul Rouf; Anam, Syaiful
Indonesian Journal of Mathematics and Applications Vol. 2 No. 2 (2024): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2024.002.02.3

Abstract

 Invariant theory can be combined with coding theory to analyze the polynomial ring over its weight enumerator. For a certain class code, especially for self-dual doubly even code or type II code, the polynomials over its code satisfy the invarian condition. In this paper, we will  show that the ring of the weight enumerator over integer of self-dual doubly even code $d_{48}^+$ cannot be ganerated by the weight enumerator of self-dual doubly even code with code length n=8, 16, 24, 32 and 40. 
Co-Authors Abdul Rouf Alghofari NUR HAMID Syaiful Anam