Macwilliams Identity for M-Spotty Hamming Weight Enumerator Over the Ring F2+ vF2
نویسندگان
چکیده
The m-spotty byte error control codes can correct or detect multiple spotty byte errors that are distributed in multiple bytes. These codes are successfully applied to computer memory systems that use RAM chips with b-bit Input/Output data when high-energy particles strike a particular RAM chips. In this paper, we derive a MacWilliams type identity for m-spotty Hamming weight enumerator over the ring F2 + vF2 with v 2 = v. 2010 Mathematics Subject Classifications: 94B15
منابع مشابه
MacWilliams type identities for some new $m$-spotty weight enumerators over finite commutative Frobenius rings
Past few years have seen an extensive use of RAM chips with wide I/O data (e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly vulnerable to a special type of byte error, called an m-spotty byte error, which can be effectively detected or corrected using byte errorcontrol codes. The MacWilliams identity provides the relationship between the weight distribution of a code and...
متن کاملMacWilliams Identity for m-spotty Weight Enumerators over Finite Ring ⋆
Recently, the m-spotty byte error control codes are used in computer memory systems to detect and correct errors. These codes are essential to make the memory systems more reliable. In this paper, we introduce the m-spotty weights and m-spotty weight enumerator of linear codes over the ring Fp[u]/(u s). Moreover, we prove a MacWilliams type identity for m-spotty weight enumerator.
متن کاملMacWilliams identities for m-spotty weight enumerators of codes over rings
Computer memory systems using high-density RAM chips are vulnerable to m-spotty byte errors when they are exposed to high-energy particles. These errors can be effectively detected or corrected using (m-spotty) byte error-control codes. In order to study the properties of these codes and to measure their error-detection and error-correction performance, m-spotty weight enumerators are introduce...
متن کاملThe MacWilliams identity for $m$-spotty weight enumerator over $\mathbb{F}_2+u\mathbb{F}_2+\cdots+u^{m-1}\mathbb{F}_2$
Past few years have seen an extensive use of RAM chips with wide I/O data (e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly vulnerable to a special type of byte error, called an m-spotty byte error, which can be effectively detected or corrected using byte error-control codes. The MacWilliams identity provides the relationship between the weight distribution of a code an...
متن کاملFinite Commutative Rings with a MacWilliams Type Relation for the m-Spotty Hamming Weight Enumerators
Let R be a finite commutative ring. We prove that a MacWilliams type relation between the m-spotty weight enumerators of a linear code over R and its dual hold, if and only if, R is a Frobenius (equivalently, Quasi-Frobenius) ring, if and only if, the number of maximal ideals and minimal ideals of R are the same, if and only if, for every linear code C over R, the dual of the dual C is C itself...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012