Allerton 2015 Paper Abstract

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Paper ThA3.1

V., Lalitha (International Institute of Information Technology, Hyderabad), Lokam, Satyanarayana V. (Microsoft Research, Bangalore)

Weight Enumerators and Higher Support Weights of Maximally Recoverable Codes

Scheduled for presentation during the Regular Session "Data Storage" (ThA3), Thursday, October 1, 2015, 08:30−08:50, Butternut

53rd Annual Allerton Conference on Communication, Control, and Computing, Sept 29-Oct 2, 2015, Allerton Park and Retreat Center, Monticello, IL, USA

This information is tentative and subject to change. Compiled on November 19, 2019

Keywords Data Storage, Coding Theory, Coding Techniques and Applications

Abstract

A code is said to be data-local maximally recoverable if (i) all the information symbols have locality and (ii) any erasure pattern which can be potentially recovered (i.e., the number of equations is equal to the number of unknowns) is recovered by the code. A code is said to be local maximally recoverable if (i) all the symbols of the code have locality and (ii) from the above holds. In this paper, we establish the matroid structures corresponding to data-local and local maximally recoverable codes (MRC). The matroid structures of these codes can be used to determine the associated Tutte polynomial. Greene proved that the weight enumerators of any code can be determined from its associated Tutte polynomial. We will use this result to derive explicit expressions for the weight enumerators of data-local MRC. Also, Britz proved that the higher support weights of any code can be determined from its associated Tutte polynomial. We will use this result to derive expressions for the higher support weights of data-local and local MRC with two local codes.

 

 

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