{
  "annotation_id": "2d92a352-aad7-4803-8bb5-41f291edd1ff",
  "date_created": "2026-02-17T05:53:26.424000Z",
  "date_modified": "2026-02-17T05:53:26.424000Z",
  "file_hash": "93b4ae128ff62b0b7b13479dbe452323bb4a097795903e57ef8576bd1692e88e",
  "private": false,
  "record": {
    "abstract": "Maximum-distance-separable (MDS) codes are widely used in distributed storage, yet naive repair of a single erasure in an $[n,k]$ MDS code downloads the entire contents of $k$ nodes. Minimum Storage Regenerating (MSR) codes (Dimakis et al., 2010) minimize repair bandwidth by contacting $d\u003ek$ helpers and downloading only a fraction of data from each. Guruswami and Wootters first proposed a linear repair scheme for Reed-Solomon (RS) codes, showing that they can be repaired with lower bandwidth than the naive approach. The existence of RS codes achieving the MSR point (RS-MSR codes) nevertheless remained open until the breakthrough construction of Tamo, Barg, and Ye, which yields RS-MSR codes with subpacketization $\\ell = s \\prod_{i=1}^n p_i$, where $p_i$ are distinct primes satisfying $p_i \\equiv 1 \\pmod{s}$ and $s=d+1-k$.\n  In this paper, we present an improved construction of RS-MSR codes by eliminating the congruence condition $p_i \\equiv 1 \\pmod{s}$. Consequently, our construction reduces the subpacketization by a multiplicative factor of $\\phi(s)^n$ ( $\\phi(\\cdot)$ is Euler\u0027s totient function) and broadens the range of feasible parameters for RS-MSR codes.",
    "arxiv_id": "2601.10685",
    "authors": [
      "Jing Qiu",
      "Weijun Fang",
      "Shu-Tao Xia",
      "Fang-Wei Fu"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Improved Constructions of Reed-Solomon Codes with Optimal Repair Bandwidth",
    "url": "https://arxiv.org/abs/2601.10685",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "377fb64b-2091-499d-9663-53283d34a867",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}