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- W1567482655 abstract "This work considers relations, which connect weight enumerator of a linear code ( mathcal{L} subset mathbb{F}_p^n ) and weight enumerator of code ( mathcal{K} ) , lying between ( mathcal{L} ) and ( mathbb{F}_p^n :mathcal{L} subseteq mathcal{K} subseteq mathbb{F}_p^n ) . The connection is establish by code ( mathcal{L}^ bot left( mathcal{K} right) ) , which is dual code of code ( mathcal{L} ) in the code ( mathcal{K} ) . It has been show, that there is a code ( mathcal{L}^ bot left( mathcal{K} right) ) , which dimension is k−l, where l and k are dimensions of ( mathcal{L} ) and ( mathcal{K} ) respectively. These relations for weight enumerators generalise the MacWilliams relation, in which ( mathcal{K} = mathbb{F}_p^n ).The new relations are written for linear code of length 2n of code ( mathcal{L} = left{ {left( {aleft| {a + b} right.} right),a in mathcal{L}_1 ,b in mathcal{L}_2 } right} ) , where ( mathcal{L}_1 ,mathcal{L}_2 subseteq mathbb{F}_p^n ) for two different comprehensive codes ( mathcal{K} ). As a result we obtain two different expressions for weight enumerator of code ( mathcal{L} ).As example we consider a case ( mathcal{L}_1 = RM_{m - 2.m} ,mathcal{L}_2 = RM_{1.m} ), where RM r.m is the r-th order Reed-Muller code of lenght n = 2m.1" @default.
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- W1567482655 date "2003-01-01" @default.
- W1567482655 modified "2023-09-27" @default.
- W1567482655 title "Relative Duality in MacWilliams Identity" @default.
- W1567482655 cites W2067474304 @default.
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- W1567482655 doi "https://doi.org/10.1007/3-540-44828-4_13" @default.
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