Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication beten storage nodes. There is a close connection beten almost affine LRCs and matroid theory which can be utilized to construct good LRCs and derive bounds on their performance. A generalized Singleton bound for linear LRCs with parameters (n; k; d; r; δ) was given in [N. Prakash et al., “Optimal Linear Codes with a Local-Error-Correction Property”, IEEE Int. Symp. Inf. Theory]. , a LRC achieving this bound is called perfect. Results on the existence and nonexistence of linear perfect (n; k; d; r; δ)-LRCs re given in [W. Song et al., “Optimal locally repairable codes”, IEEE J. Sel. Areas Comm.]. Using matroid theory, these existence and nonexistence results re later strengthened in [T. sterback et al., “On the Combinatorics of Locally Repairable Codes”, Arxiv: 1501.00153], which also provided a general lor bound on the maximal achievable minimum distance dmax(n; k; r; δ) that a linear LRC with parameters (n; k; r; δ) can have. This article expands the class of parameters (n; k; d; r; δ) for which there exist perfect linear LRCs and improves the lor bound for d max (n; k; r; δ). Further, this bound is proved to be optimal for the class of matroids that is used to derive the existence bounds of linear LRCs.
['Antti Pöllänen', 'Thomas Westerbäck', 'Ragnar Freij-Hollanti', 'Camilla Hollanti']
I am writing a research paper on a idea Bounds on the maximal minimum distance of linear locally repairable codes
[{"from": "human", "value": "I am writing a research paper on a idea Bounds on the maximal minimum distance of linear locally repairable codes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication beten storage nodes. There is a close connection beten almost affine LRCs and matroid theory which can be utilized to construct good LRCs and derive bounds on their performance. A generalized Singleton bound for linear LRCs with parameters (n; k; d; r; \u03b4) was given in [N. Prakash et al., \u201cOptimal Linear Codes with a Local-Error-Correction Property\u201d, IEEE Int. Symp. Inf. Theory]. , a LRC achieving this bound is called perfect. Results on the existence and nonexistence of linear perfect (n; k; d; r; \u03b4)-LRCs re given in [W. Song et al., \u201cOptimal locally repairable codes\u201d, IEEE J. Sel. Areas Comm.]. Using matroid theory, these existence and nonexistence results re later strengthened in [T. sterback et al., \u201cOn the Combinatorics of Locally Repairable Codes\u201d, Arxiv: 1501.00153], which also provided a general lor bound on the maximal achievable minimum distance dmax(n; k; r; \u03b4) that a linear LRC with parameters (n; k; r; \u03b4) can have. This article expands the class of parameters (n; k; d; r; \u03b4) for which there exist perfect linear LRCs and improves the lor bound for d max (n; k; r; \u03b4). Further, this bound is proved to be optimal for the class of matroids that is used to derive the existence bounds of linear LRCs."}]