A Lower Bound for Generalized Hamming Weights and a Condition for t-th Rank MDS
スポンサーリンク
概要
- 論文の詳細を見る
In this paper, we introduce a lower bound for the generalized Hamming weights, which is applicable to arbitrary linear code, in terms of the notion of well-behaving. We also show that any [n, k] linear code C over a finite field F is the t-th rank MDS for t such that g(C) + 1 ≤ t ≤ k where g(C) is easily calculated from the basis of F^n so chosen that whose first n - k elements generate C^⊥. Finally, we apply our result to Reed-Solomon, Reed-Muller and algebraic geometry codes on C_<ab>, and determine g(C) for each code.
- 社団法人電子情報通信学会の論文
- 1999-06-25
著者
-
Sakaniwa Kohichi
Department Of Communications And Integrated Systems Graduate School Of Science And Engineering Tokyo
-
Shibuya Tomoharu
Department of Information and Communication Sciences, Sophia University
-
Sakaniwa Kohichi
Departmen Of Communications And Integrated Systems Tokyo Institute Of Technology
-
Hasegawa R
Tokyo Inst. Technol. Tokyo Jpn
-
Hasegawa Ryo
Department Of Information And Computer Science Keio University
-
Shibuya Tomoharu
Department Of Communications And Integrated Systems Tokyo Institute Of Technology
-
Hasegawa Ryo
Department of Chemistry, Faculty of Science and Technology, Sophia University
関連論文
- Self-Dissolving Micropile Array Chip as Percutaneous Delivery System of Protein Drug
- A Higher Order Generalization of an Alias-Free Discrete Time-Frequency Analysis(Special Section on Digital Signal Processing)
- A Note on Constrained Least Squares Design of M-D FIR Filter Based on Convex Projection Techniques(Special Section on Digital Signal Processing)
- CONSTRAINED LEAST SQUARES DESIGN OF M-D FIR FILTER BASED ON CONVEX PROJECTION TECHNIQUES
- A-6-2 Modified Cancellation for Non-Binary LDPC Codes
- Encoding of Linear Codes Based on the Rearrangement of Block-Triangularized Parity-Check Matrices
- On Generalized Hamming Weights of Codes Constructed on Affine Algebraic Varieties (Special Section on Information Theory and Its Applications)
- On the Comparison of Lower Bounds for Generalized Hamming Weights
- Fast Acquisition of PN Sequences in DS-CDMA Systems with Incoherent Demodulator(Wireless Communication Technologies)
- Fast Acquisition of PN Sequences in DS/CDMA Systems(Regular Section)
- An Associative Memory Neural Network to Recall Nearest Pattern from Input
- Simple Estimation for the Dimension of Subfield Subcodes of AG Codes
- An Improved Bound for the Dimension of Subfield Subcodes
- A Simple Nonlinear Pre-Filtering for a Set-Theoretic Linear Blind Deconvolution Scheme(Special Section on Digital Signal Processing)
- A Set-Theoretic Blind Image Deconvolution Based on Hybrid Steepest Descent Method (Special Section on Digital Signal Processing)
- Multi-edge type LDPC code ensembles with exponentially few codewords of linear small weight (情報理論)
- A note on analytical solution of covariance evolution for regular LDPC codes (情報理論)
- Performance Analysis of LDPC Code Ensembles with Support Weight Distribution
- A-6-1 Design of Irregular LDPC Codes with Uniform Check Node Degree Distributions
- Design of IRA codes with Joint Degree Distributions
- Iterative Decoding Based on the Concave-Convex Procedure(Coding Theory)
- Justesen-Type Modified Expander Codes and Their Decoding Algorithm(Coding Theory, Information Theory and Its Applications)
- On the Performance of Algebraic Geometric Codes
- A Note on Robust Adaptive Volterra Filtering Based on Parallel Subgradient Projection Techniques(Digital Signal Processing)
- A Lower Bound for Generalized Hamming Weights and a Condition for t-th Rank MDS
- Two-Stage Random-Access Using Two-Hop Relay for Multi-Hop Systems(Spread Spectrum,Information Theory and Its Applications)
- Some Classes of Quasi-Cyclic LDPC Codes : Properties and Efficient Encoding Method(Coding Theory)
- On the size of circulant matrices for which reversible codes exist (ワイドバンドシステム)
- Construction of Cyclic Codes Suitable for Iterative Decoding via Generating Idempotents
- Characterization of Factor Graph by Mooij's Sufficient Condition for Convergence of the Sum-Product Algorithm
- Improvement of Extended Symbol-Aided Estimation for Rayleigh Fading Channels (Special Section on Information Theory and Its Applications)
- Sufficient conditions for convergence of the sum-product decoding (情報理論)
- On the size of circulant matrices for which reversible codes exist (情報処理)
- Sufficient conditions for convergence of the sum-product decoding (情報セキュリティ)
- On the size of circulant matrices for which reversible codes exist (情報セキュリティ)
- Sufficient conditions for convergence of the sum-product decoding (ワイドバンドシステム)
- Rate-Compatible Non-Binary LDPC Codes for Rate Adaptive Systems
- Analysis of Stopping Constellation Distribution for Irregular Non-binary LDPC Code Ensemble
- Ring Theoretic Approach to Reversible Codes Based on Circulant Matrices
- Design and Performance of Rate-Compatible Non-binary LDPC Convolutional Codes
- Spatially Coupled Protograph-Based LDPC Codes for Decode-and-Forward in Erasure Relay Channel
- On the dependence of error performance of spatially coupled LDPC codes on their design parameters
- Effects of additives on photo-methoxylation of methyl 2-pyridinecarboxylate in acidic methanolic solutions. Promotion by 4-substituted pyridines.
- On the Dependence of Error Performance of Spatially Coupled LDPC Codes on Their Design Parameters