A classification of MDS binary systematic codes
نویسنده
چکیده
Binary MDS linear codes are well-known. We prove that any binary MDS systematic non-linear code is equivalent to a linear code and hence we classify them completely.
منابع مشابه
Enabling All-Node-Repair in Minimum Storage Regenerating Codes
We consider the problem of constructing exact-repair minimum storage regenerating (MSR) codes, for which both the systematic nodes and parity nodes can be repaired optimally. Although there exist several recent explicit high-rate MSR code constructions (usually with certain restrictions on the coding parameters), quite a few constructions in the literature only allow the optimal repair of syste...
متن کاملElias Upper Bound for Euclidean Space Codes and Codes Close to the Singleton Bound
A typical communication system consists of a channel code to transmit signals reliably over a noisy channel. In general the channel code is a set of codewords which are used to carry information over the channel. This thesis deals with Elias upper bound on the normalized rate for Euclidean space codes and on codes which are close to the generalized Singleton bound, like MaximumDistance Separabl...
متن کاملar X iv : c s . IT / 0 50 50 54 v 1 2 1 M ay 2 00 5 The Partition Weight Enumerator of MDS Codes and its Applications
A closed form formula of the partition weight enumerator of maximum distance separable (MDS) codes is derived for an arbitrary number of partitions. Using this result, some properties of MDS codes are discussed. The results are extended for the average binary image of MDS codes in finite fields of characteristic two. As an application, we study the multiuser error probability of Reed Solomon co...
متن کاملEuclidean and Hermitian LCD MDS codes
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault injection attacks. Non-binary LCD codes in characteristic 2 can be transformed into binary LCD codes by expansion. On the other hand, being optimal codes, maxim...
متن کاملOn the Multiuser Error Probability and the Maximum Likelihood Performance of MDS Codes
MDS (e.g. Reed-Solomon) codes have many desirable properties which make them the code of choice in network scenarios and distributed coding schemes. An average binary weight enumerator of Reed-Solomon (RS) codes is derived assuming a binomial distribution of the bits in a non-zero symbol. Lower bounds on the average binary minimum distance of the ensemble of binary images of a Reed-Solomon code...
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 2006