chapter, introduction, background, thesis, deals, data, storage, distributed, systems, stored, servers, operate, independently, example, consisting, nservers, assume, user, multiple, further, consider, scenario, situation, requests, satised, redundantly, described, preceding, paragraph, formalized, locally, repairable, codes, lrcs, allow, local, repair, symbols, process, recovering, erased, set, setup, encoded, failed, mapped, literature, review, standard, notations, classical, coding, theory, drefer, length, dimension, minimum, dened, nite, eld, respectively, notion, locality, recovered, introduced, yekhanin, et, al, performed, depth, study, relationships, redundancy, following, main, results, rdenotes, information, repaired, rother, recognizing, unsuccessful, rsymbols, wang, zhang, introduce, availability, tdisjoint, derive, upper, bound, linearcodes, re, write, below, derived, dimakis, non, tamo, barg, deriving, symbollocality, obtain, generalized, mazumdar, cooperative, used, recover, disjoint, ldenotes, erasures, zdenotes, maximum, required, contribution, introducing, generalization, named, multi, rcs, dierent, construction, collection, repetitions, allowed, mlrcs, compare, existing, organization, models, address, section, brief, overview, necessary, readers, unfamiliar, concepts, relevant, generic, established, title, suggests, brie, comment, research, sequence, sequentially, advanced, speed, remaining, encouraged, abbreviated, clrcs, preliminaries, avia, message, brock, represent, kbit, vector, fk, ideally, medium, errors, receive, intended, however, noisy, likely, ipped, transmission, accounts, issue, correcting, simply, transmitted, particular, linear, codeword, space, matrix, called, generator, matrixof, fol, lowing, wil, cal, led, encoding, avias, encodedto, simplex, xis, using, generate, immediately, rst, yare, viz, coincidence, encode, directly, referred, systematic, normally, parameters, within, brackets, d], represented, equals, kis, usually, nmatrix, linearly, independent, hamming, coordinates, dier, instance, formally, written, jfi, igj, denotes, aand, ja, denoted, nonlinear, cconsisting, combination, ccan, fy, captured, richard, collom, singleton, binary, yis, reconstruct, th, indices, possibilities, equations, groupsof, union, intersecting, consideration, needed, thus, yhas, total, denition, satises, properties, trepair, exist, tsets, function, indexed, [k, [n, ]nf, ig, [t, ysuch, obvious, showing, listed, de, contains, fth, discussion, given, intersect, shown, studied, codewordy, zother, sj, remains, demonstrate, minor, amendment, proof, theorem, tighter, perform, detailed, basics, tnon, tuple, oftsymbols, elements, necessarily, distinct, reconstructed, ]n, tg, discuss, yencodes, argue, discussing, choices, allowing, claim, seventh, eighth, ninth, tenth, mentioned, convince, rt, tand, appeared, later, optimize, require, letcbe, cby, constructing, sub, xed, remove, smaller, min, dmin, inequality, analysis, describe, based, techniques, pro, ject, onto, chosen, iteration, jection, popular, correspond, construct, repeated, loop, dene, tothe, ij, [j, inthe, aj, jj, relations, jin, algorithm, input, jc, choose, fij, tindices, letr, jbe, rtcode, tsymbols, lety, fj, frequent, xj, maximal, subset, jand, replace, occurrences, jby, output, consists, jr, qj, truncated, factor, induction, base, assuming, terminates, log, qjc, qqp, recall, j[, plugged, leading, noting, ji, formed, puncturing, applying, combining, nally, corollary, cmust, greater, tto, terasures, yields, optimizing, presented, estimate, value, adjustment, term, penalty, adding, atop, taking, derivative, respect, ignoring, ceiling, operation, equating, zero, plugging, incurred, pmlrc, plrc, kt, restrictive, expect, tinto, te, dte, comparison, lrepresents, zrepresents, translate, pclrc, kand, noticed, worst, mandatorily, reasonable, extension, balancing, requirements, necessitate, haveconcentrated, adapting, possible, acknowledgments, express, sincere, gratitude, european, commission, funding, participation, nordsecmob, program, dr, vitaly, skachek, guidance, hui, helpful, appreciate, support, baba, mamu, shubu