Error-Correction of Multidimensional Bursts

A construction for D-dimensional binary codes of size n₁timesn₂timeshelliptimesn_D correcting a single D-dimensional box error is presented. If the size of the box error is b₁timesb₂timeshelliptimesb_D, b_i odd, 1les i les D, and B = Pi_i ^D=₁b_i, then the redundancy of the code is at most [log₂(n₁n₂hellip n_D)] +B + (D-2)[log₂ B] + [log₂b₁]. For a two-dimensional binary array of size n times n we present a code correcting an error whose shape is a Lee sphere with radius R. The redundancy of the code is at most [log₂n²] + 2R² + 2R + [2log₂ (2R+1)]+1. This is also the redundancy of a binary code which corrects an arbitrary two-dimensional cluster-error of size 2R+1. A generalization for D-dimensional code which corrects either D-dimensional error whose shape is a Lee sphere or an arbitrary cluster-error is also given.