Cyclic Hamming codes and their relatives
On additive cyclic codes
... Linear codes are the most important classes of codes and widely studied because of their algebraic structure, which provides easier ...implementation. Cyclic codes form a fundamental subclass ...
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Generalized DNA Barcode Design Based on Hamming Codes
... linear codes are quite suitable for this ...linear codes, their contribution to the sequencing noise is at least 10 times lower compared to substitutions ...linear codes is in its simplicity as well ...
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CONSTRUCTION OF REGULAR QUASI CYCLIC-LOW DENSITY PARITY CHECK CODES FROM CYCLIC CODES
... derived cyclic code; we have reduced in half the incidence vectors of matrix H LDPC and have improved the error-correcting performance of QC-LDPC ...LDPC codes have high density, high rates and the ...
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Algebraic methods for the distance of cyclic codes
... 1.2 Cyclic codes In this section we introduce the principal aspects concerning an important subclass of linear codes: cyclic ...these codes, in fact from an algebraic point of view, the ...
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Z_2-Triple Cyclic Codes and Their Duals
... Z 2 [x] hx r −1i × hx Z s 2 −1i [x] × hx Z t 2 −1i [x] , in polynomial representation. In this paper, we determine the structure of these codes. We have obtained the form of the generators for such codes. ...
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A Class of Three-Weight Cyclic Codes
... the cyclic codes with parity-check polynomials h 1 (x)h 2 (x) are ...the cyclic codes are also optimal. The three-weight cyclic codes dealt with in this paper may have ...
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Low complexity decoding of cyclic codes.
... tions outside die syndrome window. For the category of minimum displacement of 6, there are two possible solutions if a single cover position is considered. It could be position 5 or 6 as they also cover three ...
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Explicit Computation of Generalized Hamming Weights for Some Algebraic Geometric Codes
... Ž . the curves see Theorem 1.4 . In Section 2, we prove our main results, Theorems 2.3 and 2.2. In Section 3, we study the generalized Hamming weights for Fermat curves. To make our paper more self-contained, we ...
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Low-Density Parity-Check Codes and their Rateless Relatives
... turbo codes. In this survey, we will only focus our attention on LDPC codes and their rateless ...LDPC codes, such as their encoding and decoding techniques, the convergence of their decoding and the ...
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p-Adic estimates of Hamming weights in Abelian codes over Galois rings
... of Hamming Weights in Abelian Codes Over Galois Rings Daniel ...of Hamming weights of words in cyclic codes is proved in this paper by means of counting polynomial techniques introduced ...
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Low-Floor Tanner Codes via Hamming-Node or RSCC-Node Doping
... and cyclic-2 PML decoders are both SISO list-based decoders. Cyclic-2 has an advantage over modified Chase in term of complexity as it uses a list that refers to nearby codewords, which are independent of ...
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Cyclic Codes: Low-Weight Codewords and Locators
... correcting codes has become an integral part of the design of reliable data transmis- sions and storage ...correcting codes are also playing an increasingly important role for other applications such as the ...
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On Skew Cyclic Codes over a Finite Ring
... Recently, there has been a vast interests on the study of cyclic codes. It is mainly due to their applications in power management [21], secret sharing [24, 23], steganography [14], etc. Also, these ...
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Enhanced Detection Of Double Adjacent Errors In Hamming Codes Through Selective Bit Placement
... correction codes (ECCs), Hamming codes. I. INTRODUCTION Hamming codes are a family of linear error-correcting codes, generalize the Hamming code invented by Richard ...
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A parallel Viterbi decoder for block cyclic and convolution codes
... least Hamming distance of the codeword that is legitimately generated via state R for the ith input bit, from the actual input ...a Hamming distance less than or equal to the minimum code separation, d min ...
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On the lattice of cyclic codes over finite chain rings
... ℓ−1 X j=0 c j X j + hX ℓ − 1i (1) where hX ℓ − 1i is the ideal of R[X] generated by X ℓ − 1. The ideal Ψ(C) is called the polynomial representation of C, and this polynomial representation was used in [3, 5, 10, 13, 14] ...
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Efficient Encryption from Random Quasi-Cyclic Codes
... from codes that do not hide any structure in their public ...linear codes from random errors of low ...the Hamming Quasi-Cyclic cryptosystem (HQC), based on the Hamming metric, and the ...
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Chapter 1. Search for Good Linear Codes in the Class of Quasi-Cyclic and Related Codes
... block codes such as cyclic codes, BCH codes, Reed-Solomon codes, Hamming codes, quadratic residue codes, and quasi-cyclic (QC) ...QC codes and open ...
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Modified Hamming Codes with Double Adjacent Error Correction along with Enhanced Adjacent Error Detection
... correction codes are used in semiconductor memories to protect information against soft ...correction codes are preferred due to their simple encoding/decoding logic, low redundancy and low ...
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Flag fault-tolerant error correction for cyclic CSS codes
... all cyclic CSS codes are Hamming codes and therefore the methods in [5] cannot be directly applied, thus providing further motivation for our ...
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