An identity between the m-spotty weight enumerators of a linear code and its dual

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

The m-spotty byte error control codes provide a good source for detecting and correcting errors in semiconductor memory systems using high density RAM chips with wide I/O data (e.g. 8, 16, or 32 bits). m-spotty byte error control codes are very suitable for burst correction. Here, we introduce the m-spotty weights and m-spotty weight enumerator of linear codes over the ring F2+uF2 and prove a MacWilliams type identity.

Anahtar Kelimeler:

Linear codes over F2+uF2, m-spotty weights, MacWilliams identity

An identity between the m-spotty weight enumerators of a linear code and its dual

Keywords:

Linear codes over F2+uF2, m-spotty weights, MacWilliams identity,

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Table 2. The codewords and the corresponding terms. Codewords v1 v F0(z)F1(z)F2(z)F3(z) F0(z)F(z) = 1 + 72z + 1350z+ 1944z3+ 729z4
F2(z)F(z) = 1 + 32z− 114z2+ 81z4 F2(z)F2(z) = 1− 8z + 22z2− 24z3+ 9z4 F1(z)F1(z) = 1 + 16z + 46z2− 144z3+ 81z4 F(z)F3(z) = 1 + 8z− 10z2− 8z3+ 9z4 F3(z)F3(z) = 1− 2z2+ z4 (i = 11, 12, 15, 16) vi F0(z) = 1 + 36z + 27z2,F1(z) = 1 + 8z− 9z2, F2(z) = 1− 4z + 3z2, and F3(z) = 1− z2.