the paper presents lower and upper bounds on the number of parity check digits required for a linear code that detects solid bursts of length $b$ or less and simultaneously any $e$ or less random errors. an example of such a code is also provided. further, codes capable of detecting and simultaneously correcting such errors have also been dealt with.

background: in some verses in holy quran; 233 surat al-baghare , 15 al-ahghaf , 14 loghman and 6 al-talagh, breastfeeding, gravidity, and parity recommended to the parents and expected their children to be accountable to the parents; particularly to mothers due to tolerate of pregnancy and breastfeeding duration. methods: the case-control study included 376 patients diagnosed between      2001-...

Three constructions of minimum storage regenerating (MSR) codes are presented. The first two constructions provide access-optimal MSR codes, with two and three parities, respectively, which attain the sub-packetization bound for access-optimal codes. The third construction provides larger MSR codes with three parities, which are not access-optimal, and do not necessarily attain the sub-packetiz...

In [1] nested codes are defined and some fundamental properties are introduced. We review the usage of nested codes in wyner’s noiseless binning scheme,noisy side information problems and dirty paper problems. Some related topic such as multiterminal coding of correlated sources and coordinated encoding over mutually interfering channels are also touched. I. NESTED CODES: PRELIMINARIES Nested c...

We describe and analyze the joint source/channel coding properties of a class of sparse graphical codes based on compounding a low-density generator matrix (LDGM) code with a low-density parity check (LDPC) code. Our first pair of theorems establish that there exist codes from this ensemble, with all degrees remaining bounded independently of block length, that are simultaneously optimal as bot...

We examine the security of several digital signature schemes based on algebraic block codes. It is shown that Xinmei’s digital signature scheme cau be totally broken by a known plaintext attack with complexity O(k3), where t is the dimension of the code used in the scheme. Harn and Wang have proposed a modified version of Xinmei’s scheme that prevents selective forgeries. Their scheme is also s...

A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudorandom nature, and the new codes are quasi-cyclic. Graph isomorphisms and automorphisms are identified and used in an efficient search for good codes. Graphs with girth as large as 12 wer...

We present a scheme for erasure decoding of AG-codes of complexity O(n2). This improves on methods involving Fourier transforms. The trivial scheme for erasure decoding of AG-codes (Algebraic Geometry codes in full, or Geometric Goppa codes) solves a system of linear equations. The scheme is of complexity O(n), where n denotes the codelength. Fast schemes, that use a Fourier transform of all sy...

This paper introduces a novel binary, long double error correcting, systematic code (8 2 5) that can detect and correct errors up to two bits in the received vector using simple concept of syndrome decoding. The motivation behind the construction of this code is the idea to achieve 100% error correction on the receiver side and to use the encoder/decoder that is simpler than the existing double...

This thesis presents new techniques for the construction and specification of linear tail-biting trellises. Tail-biting trellises for linear block codes are combinatorial descriptions in the form of layered graphs, that are somewhat more compact than the corresponding conventional trellis descriptions. Conventional trellises for block codes have a well understood underlying theory. On the other...