Random Simplicial Complexes and the Construction of Linear Error Correcting Codes
نویسنده
چکیده
منابع مشابه
Constacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملA Generalization of the Parallel Error Correcting Codes by Allowing Some Random Errors
This paper generalizes parallel error correcting codes proposed by Ahlswede et al. over a new type of multiple access channel called parallel error channel. The generalized parallel error correcting codes can handle with more errors compared with the original ones. We show construction methods of independent and non-independent parallel error correcting codes and decoding methods. We derive som...
متن کاملOne-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes
We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...
متن کاملOn t-Error Correcting/All Unidirectional Error Detecting Codes
We present families of binary systematic codes that can correct t random errors and detect more than t unidirectional errors. As in recent papers, we start by encoding the k information symbols into a codeword of an [n', k, 2t + 11 error correcting code. The second step of our construction involves adding more bits to this linear error correcting code in order to obtain the detection capability...
متن کاملConstructing Quantum Error-Correcting Codes for p-State Systems from Classical Error-Correcting Codes∗
Quantum error-correcting codes have attracted much attention. Among many research articles, the most general and systematic construction is the so called stabilizer code construction [6] or additive code construction [2], which constructs a quantum error-correcting code as an eigenspace of an Abelian subgroup S of the error group. Thereafter Calderbank et al. [3] proposed a construction of S fr...
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 2010